\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Find the oblique (slant) asymptote of \(\displaystyle f(x) = \frac{x^{3} + x^{2} - 69 x - 189}{x^{2} + 17 x + 72}\).
The oblique asymptote is the whole part without the remainder after polynomial long division.
\begin{question}Find the oblique (slant) asymptote of $f(x) = \frac{x^{3} + x^{2} - 69 x - 189}{x^{2} + 17 x + 72}$.
\soln{9cm}{The oblique asymptote is the whole part without the remainder after polynomial long division. \newline
\begin{center}\begin{tikzpicture}
\draw (0,0) node{$ \polylongdiv{x^3 + x^2 - 69*x - 189}{x^2 + 17*x + 72} $};
\end{tikzpicture}
\end{center}
Dividing gives the quotient $x - 16$ and the remainder $131 x + 963$. The oblique asymptote is $y = x - 16$. }
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Find the oblique (slant) asymptote of <img class="equation_image" title=" \displaystyle f(x) = \frac{x^{3} + x^{2} - 69 x - 189}{x^{2} + 17 x + 72} " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20%5Cfrac%7Bx%5E%7B3%7D%20%2B%20x%5E%7B2%7D%20-%2069%20x%20-%20189%7D%7Bx%5E%7B2%7D%20%2B%2017%20x%20%2B%2072%7D%20" alt="LaTeX: \displaystyle f(x) = \frac{x^{3} + x^{2} - 69 x - 189}{x^{2} + 17 x + 72} " data-equation-content=" \displaystyle f(x) = \frac{x^{3} + x^{2} - 69 x - 189}{x^{2} + 17 x + 72} " /> . </p> </p><p> <p>The oblique asymptote is the whole part without the remainder after polynomial long division. <br>
<center><?xml version="1.0" encoding="UTF-8"?>
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="173.051pt" height="15.581pt" viewBox="0 0 173.051 15.581" version="1.1">
<defs>
<g>
<symbol overflow="visible" id="glyph0-0">
<path style="stroke:none;" d=""/>
</symbol>
<symbol overflow="visible" id="glyph0-1">
<path style="stroke:none;" d="M 3.328125 -3.015625 C 3.390625 -3.265625 3.625 -4.1875 4.3125 -4.1875 C 4.359375 -4.1875 4.609375 -4.1875 4.8125 -4.0625 C 4.53125 -4 4.34375 -3.765625 4.34375 -3.515625 C 4.34375 -3.359375 4.453125 -3.171875 4.71875 -3.171875 C 4.9375 -3.171875 5.25 -3.34375 5.25 -3.75 C 5.25 -4.265625 4.671875 -4.40625 4.328125 -4.40625 C 3.75 -4.40625 3.40625 -3.875 3.28125 -3.65625 C 3.03125 -4.3125 2.5 -4.40625 2.203125 -4.40625 C 1.171875 -4.40625 0.59375 -3.125 0.59375 -2.875 C 0.59375 -2.765625 0.703125 -2.765625 0.71875 -2.765625 C 0.796875 -2.765625 0.828125 -2.796875 0.84375 -2.875 C 1.1875 -3.9375 1.84375 -4.1875 2.1875 -4.1875 C 2.375 -4.1875 2.71875 -4.09375 2.71875 -3.515625 C 2.71875 -3.203125 2.546875 -2.546875 2.1875 -1.140625 C 2.03125 -0.53125 1.671875 -0.109375 1.234375 -0.109375 C 1.171875 -0.109375 0.953125 -0.109375 0.734375 -0.234375 C 0.984375 -0.296875 1.203125 -0.5 1.203125 -0.78125 C 1.203125 -1.046875 0.984375 -1.125 0.84375 -1.125 C 0.53125 -1.125 0.296875 -0.875 0.296875 -0.546875 C 0.296875 -0.09375 0.78125 0.109375 1.21875 0.109375 C 1.890625 0.109375 2.25 -0.59375 2.265625 -0.640625 C 2.390625 -0.28125 2.75 0.109375 3.34375 0.109375 C 4.375 0.109375 4.9375 -1.171875 4.9375 -1.421875 C 4.9375 -1.53125 4.859375 -1.53125 4.828125 -1.53125 C 4.734375 -1.53125 4.71875 -1.484375 4.6875 -1.421875 C 4.359375 -0.34375 3.6875 -0.109375 3.375 -0.109375 C 2.984375 -0.109375 2.828125 -0.421875 2.828125 -0.765625 C 2.828125 -0.984375 2.875 -1.203125 2.984375 -1.640625 Z M 3.328125 -3.015625 "/>
</symbol>
<symbol overflow="visible" id="glyph1-0">
<path style="stroke:none;" d=""/>
</symbol>
<symbol overflow="visible" id="glyph1-1">
<path style="stroke:none;" d="M 1.90625 -2.328125 C 2.453125 -2.328125 2.84375 -1.953125 2.84375 -1.203125 C 2.84375 -0.34375 2.328125 -0.078125 1.9375 -0.078125 C 1.65625 -0.078125 1.03125 -0.15625 0.75 -0.578125 C 1.078125 -0.578125 1.15625 -0.8125 1.15625 -0.96875 C 1.15625 -1.1875 0.984375 -1.34375 0.765625 -1.34375 C 0.578125 -1.34375 0.375 -1.21875 0.375 -0.9375 C 0.375 -0.28125 1.09375 0.140625 1.9375 0.140625 C 2.90625 0.140625 3.578125 -0.515625 3.578125 -1.203125 C 3.578125 -1.75 3.140625 -2.296875 2.375 -2.453125 C 3.09375 -2.71875 3.359375 -3.234375 3.359375 -3.671875 C 3.359375 -4.21875 2.734375 -4.625 1.953125 -4.625 C 1.1875 -4.625 0.59375 -4.25 0.59375 -3.6875 C 0.59375 -3.453125 0.75 -3.328125 0.953125 -3.328125 C 1.171875 -3.328125 1.3125 -3.484375 1.3125 -3.671875 C 1.3125 -3.875 1.171875 -4.03125 0.953125 -4.046875 C 1.203125 -4.34375 1.671875 -4.421875 1.9375 -4.421875 C 2.25 -4.421875 2.6875 -4.265625 2.6875 -3.671875 C 2.6875 -3.375 2.59375 -3.046875 2.40625 -2.84375 C 2.1875 -2.578125 1.984375 -2.5625 1.640625 -2.53125 C 1.46875 -2.515625 1.453125 -2.515625 1.421875 -2.515625 C 1.40625 -2.515625 1.34375 -2.5 1.34375 -2.421875 C 1.34375 -2.328125 1.40625 -2.328125 1.53125 -2.328125 Z M 1.90625 -2.328125 "/>
</symbol>
<symbol overflow="visible" id="glyph1-2">
<path style="stroke:none;" d="M 3.515625 -1.265625 L 3.28125 -1.265625 C 3.265625 -1.109375 3.1875 -0.703125 3.09375 -0.640625 C 3.046875 -0.59375 2.515625 -0.59375 2.40625 -0.59375 L 1.125 -0.59375 C 1.859375 -1.234375 2.109375 -1.4375 2.515625 -1.765625 C 3.03125 -2.171875 3.515625 -2.609375 3.515625 -3.265625 C 3.515625 -4.109375 2.78125 -4.625 1.890625 -4.625 C 1.03125 -4.625 0.4375 -4.015625 0.4375 -3.375 C 0.4375 -3.03125 0.734375 -2.984375 0.8125 -2.984375 C 0.96875 -2.984375 1.171875 -3.109375 1.171875 -3.359375 C 1.171875 -3.484375 1.125 -3.734375 0.765625 -3.734375 C 0.984375 -4.21875 1.453125 -4.375 1.78125 -4.375 C 2.484375 -4.375 2.84375 -3.828125 2.84375 -3.265625 C 2.84375 -2.65625 2.40625 -2.1875 2.1875 -1.9375 L 0.515625 -0.265625 C 0.4375 -0.203125 0.4375 -0.1875 0.4375 0 L 3.3125 0 Z M 3.515625 -1.265625 "/>
</symbol>
<symbol overflow="visible" id="glyph2-0">
<path style="stroke:none;" d=""/>
</symbol>
<symbol overflow="visible" id="glyph2-1">
<path style="stroke:none;" d="M 4.078125 -2.296875 L 6.859375 -2.296875 C 7 -2.296875 7.1875 -2.296875 7.1875 -2.5 C 7.1875 -2.6875 7 -2.6875 6.859375 -2.6875 L 4.078125 -2.6875 L 4.078125 -5.484375 C 4.078125 -5.625 4.078125 -5.8125 3.875 -5.8125 C 3.671875 -5.8125 3.671875 -5.625 3.671875 -5.484375 L 3.671875 -2.6875 L 0.890625 -2.6875 C 0.75 -2.6875 0.5625 -2.6875 0.5625 -2.5 C 0.5625 -2.296875 0.75 -2.296875 0.890625 -2.296875 L 3.671875 -2.296875 L 3.671875 0.5 C 3.671875 0.640625 3.671875 0.828125 3.875 0.828125 C 4.078125 0.828125 4.078125 0.640625 4.078125 0.5 Z M 4.078125 -2.296875 "/>
</symbol>
<symbol overflow="visible" id="glyph2-2">
<path style="stroke:none;" d="M 1.3125 -3.265625 L 1.3125 -3.515625 C 1.3125 -6.03125 2.546875 -6.390625 3.0625 -6.390625 C 3.296875 -6.390625 3.71875 -6.328125 3.9375 -5.984375 C 3.78125 -5.984375 3.390625 -5.984375 3.390625 -5.546875 C 3.390625 -5.234375 3.625 -5.078125 3.84375 -5.078125 C 4 -5.078125 4.3125 -5.171875 4.3125 -5.5625 C 4.3125 -6.15625 3.875 -6.640625 3.046875 -6.640625 C 1.765625 -6.640625 0.421875 -5.359375 0.421875 -3.15625 C 0.421875 -0.484375 1.578125 0.21875 2.5 0.21875 C 3.609375 0.21875 4.5625 -0.71875 4.5625 -2.03125 C 4.5625 -3.296875 3.671875 -4.25 2.5625 -4.25 C 1.890625 -4.25 1.515625 -3.75 1.3125 -3.265625 Z M 2.5 -0.0625 C 1.875 -0.0625 1.578125 -0.65625 1.515625 -0.8125 C 1.328125 -1.28125 1.328125 -2.078125 1.328125 -2.25 C 1.328125 -3.03125 1.65625 -4.03125 2.546875 -4.03125 C 2.71875 -4.03125 3.171875 -4.03125 3.484375 -3.40625 C 3.65625 -3.046875 3.65625 -2.53125 3.65625 -2.046875 C 3.65625 -1.5625 3.65625 -1.0625 3.484375 -0.703125 C 3.1875 -0.109375 2.734375 -0.0625 2.5 -0.0625 Z M 2.5 -0.0625 "/>
</symbol>
<symbol overflow="visible" id="glyph2-3">
<path style="stroke:none;" d="M 3.65625 -3.171875 L 3.65625 -2.84375 C 3.65625 -0.515625 2.625 -0.0625 2.046875 -0.0625 C 1.875 -0.0625 1.328125 -0.078125 1.0625 -0.421875 C 1.5 -0.421875 1.578125 -0.703125 1.578125 -0.875 C 1.578125 -1.1875 1.34375 -1.328125 1.125 -1.328125 C 0.96875 -1.328125 0.671875 -1.25 0.671875 -0.859375 C 0.671875 -0.1875 1.203125 0.21875 2.046875 0.21875 C 3.34375 0.21875 4.5625 -1.140625 4.5625 -3.28125 C 4.5625 -5.96875 3.40625 -6.640625 2.515625 -6.640625 C 1.96875 -6.640625 1.484375 -6.453125 1.0625 -6.015625 C 0.640625 -5.5625 0.421875 -5.140625 0.421875 -4.390625 C 0.421875 -3.15625 1.296875 -2.171875 2.40625 -2.171875 C 3.015625 -2.171875 3.421875 -2.59375 3.65625 -3.171875 Z M 2.421875 -2.40625 C 2.265625 -2.40625 1.796875 -2.40625 1.5 -3.03125 C 1.3125 -3.40625 1.3125 -3.890625 1.3125 -4.390625 C 1.3125 -4.921875 1.3125 -5.390625 1.53125 -5.765625 C 1.796875 -6.265625 2.171875 -6.390625 2.515625 -6.390625 C 2.984375 -6.390625 3.3125 -6.046875 3.484375 -5.609375 C 3.59375 -5.28125 3.640625 -4.65625 3.640625 -4.203125 C 3.640625 -3.375 3.296875 -2.40625 2.421875 -2.40625 Z M 2.421875 -2.40625 "/>
</symbol>
<symbol overflow="visible" id="glyph2-4">
<path style="stroke:none;" d="M 2.9375 -6.375 C 2.9375 -6.625 2.9375 -6.640625 2.703125 -6.640625 C 2.078125 -6 1.203125 -6 0.890625 -6 L 0.890625 -5.6875 C 1.09375 -5.6875 1.671875 -5.6875 2.1875 -5.953125 L 2.1875 -0.78125 C 2.1875 -0.421875 2.15625 -0.3125 1.265625 -0.3125 L 0.953125 -0.3125 L 0.953125 0 C 1.296875 -0.03125 2.15625 -0.03125 2.5625 -0.03125 C 2.953125 -0.03125 3.828125 -0.03125 4.171875 0 L 4.171875 -0.3125 L 3.859375 -0.3125 C 2.953125 -0.3125 2.9375 -0.421875 2.9375 -0.78125 Z M 2.9375 -6.375 "/>
</symbol>
<symbol overflow="visible" id="glyph2-5">
<path style="stroke:none;" d="M 1.625 -4.5625 C 1.171875 -4.859375 1.125 -5.1875 1.125 -5.359375 C 1.125 -5.96875 1.78125 -6.390625 2.484375 -6.390625 C 3.203125 -6.390625 3.84375 -5.875 3.84375 -5.15625 C 3.84375 -4.578125 3.453125 -4.109375 2.859375 -3.765625 Z M 3.078125 -3.609375 C 3.796875 -3.984375 4.28125 -4.5 4.28125 -5.15625 C 4.28125 -6.078125 3.40625 -6.640625 2.5 -6.640625 C 1.5 -6.640625 0.6875 -5.90625 0.6875 -4.96875 C 0.6875 -4.796875 0.703125 -4.34375 1.125 -3.875 C 1.234375 -3.765625 1.609375 -3.515625 1.859375 -3.34375 C 1.28125 -3.046875 0.421875 -2.5 0.421875 -1.5 C 0.421875 -0.453125 1.4375 0.21875 2.484375 0.21875 C 3.609375 0.21875 4.5625 -0.609375 4.5625 -1.671875 C 4.5625 -2.03125 4.453125 -2.484375 4.0625 -2.90625 C 3.875 -3.109375 3.71875 -3.203125 3.078125 -3.609375 Z M 2.078125 -3.1875 L 3.3125 -2.40625 C 3.59375 -2.21875 4.0625 -1.921875 4.0625 -1.3125 C 4.0625 -0.578125 3.3125 -0.0625 2.5 -0.0625 C 1.640625 -0.0625 0.921875 -0.671875 0.921875 -1.5 C 0.921875 -2.078125 1.234375 -2.71875 2.078125 -3.1875 Z M 2.078125 -3.1875 "/>
</symbol>
<symbol overflow="visible" id="glyph2-6">
<path style="stroke:none;" d="M 4.75 -6.078125 C 4.828125 -6.1875 4.828125 -6.203125 4.828125 -6.421875 L 2.40625 -6.421875 C 1.203125 -6.421875 1.171875 -6.546875 1.140625 -6.734375 L 0.890625 -6.734375 L 0.5625 -4.6875 L 0.8125 -4.6875 C 0.84375 -4.84375 0.921875 -5.46875 1.0625 -5.59375 C 1.125 -5.65625 1.90625 -5.65625 2.03125 -5.65625 L 4.09375 -5.65625 C 3.984375 -5.5 3.203125 -4.40625 2.984375 -4.078125 C 2.078125 -2.734375 1.75 -1.34375 1.75 -0.328125 C 1.75 -0.234375 1.75 0.21875 2.21875 0.21875 C 2.671875 0.21875 2.671875 -0.234375 2.671875 -0.328125 L 2.671875 -0.84375 C 2.671875 -1.390625 2.703125 -1.9375 2.78125 -2.46875 C 2.828125 -2.703125 2.953125 -3.5625 3.40625 -4.171875 Z M 4.75 -6.078125 "/>
</symbol>
<symbol overflow="visible" id="glyph2-7">
<path style="stroke:none;" d="M 1.265625 -0.765625 L 2.328125 -1.796875 C 3.875 -3.171875 4.46875 -3.703125 4.46875 -4.703125 C 4.46875 -5.84375 3.578125 -6.640625 2.359375 -6.640625 C 1.234375 -6.640625 0.5 -5.71875 0.5 -4.828125 C 0.5 -4.28125 1 -4.28125 1.03125 -4.28125 C 1.203125 -4.28125 1.546875 -4.390625 1.546875 -4.8125 C 1.546875 -5.0625 1.359375 -5.328125 1.015625 -5.328125 C 0.9375 -5.328125 0.921875 -5.328125 0.890625 -5.3125 C 1.109375 -5.96875 1.65625 -6.328125 2.234375 -6.328125 C 3.140625 -6.328125 3.5625 -5.515625 3.5625 -4.703125 C 3.5625 -3.90625 3.078125 -3.125 2.515625 -2.5 L 0.609375 -0.375 C 0.5 -0.265625 0.5 -0.234375 0.5 0 L 4.203125 0 L 4.46875 -1.734375 L 4.234375 -1.734375 C 4.171875 -1.4375 4.109375 -1 4 -0.84375 C 3.9375 -0.765625 3.28125 -0.765625 3.0625 -0.765625 Z M 1.265625 -0.765625 "/>
</symbol>
<symbol overflow="visible" id="glyph3-0">
<path style="stroke:none;" d=""/>
</symbol>
<symbol overflow="visible" id="glyph3-1">
<path style="stroke:none;" d="M 6.5625 -2.296875 C 6.734375 -2.296875 6.921875 -2.296875 6.921875 -2.5 C 6.921875 -2.6875 6.734375 -2.6875 6.5625 -2.6875 L 1.171875 -2.6875 C 1 -2.6875 0.828125 -2.6875 0.828125 -2.5 C 0.828125 -2.296875 1 -2.296875 1.171875 -2.296875 Z M 6.5625 -2.296875 "/>
</symbol>
<symbol overflow="visible" id="glyph3-2">
<path style="stroke:none;" d="M 2.734375 -4.25 C 2.75 -4.390625 2.75 -4.640625 2.5 -4.640625 C 2.328125 -4.640625 2.203125 -4.5 2.234375 -4.375 L 2.234375 -4.25 L 2.375 -2.703125 L 1.09375 -3.625 C 1 -3.671875 0.984375 -3.703125 0.921875 -3.703125 C 0.78125 -3.703125 0.640625 -3.5625 0.640625 -3.421875 C 0.640625 -3.265625 0.75 -3.21875 0.84375 -3.171875 L 2.265625 -2.5 L 0.890625 -1.828125 C 0.734375 -1.75 0.640625 -1.703125 0.640625 -1.5625 C 0.640625 -1.40625 0.78125 -1.28125 0.921875 -1.28125 C 0.984375 -1.28125 1 -1.28125 1.25 -1.46875 L 2.375 -2.265625 L 2.21875 -0.59375 C 2.21875 -0.390625 2.40625 -0.34375 2.484375 -0.34375 C 2.609375 -0.34375 2.75 -0.40625 2.75 -0.59375 L 2.609375 -2.265625 L 3.875 -1.34375 C 3.96875 -1.296875 3.984375 -1.28125 4.0625 -1.28125 C 4.203125 -1.28125 4.328125 -1.421875 4.328125 -1.5625 C 4.328125 -1.703125 4.234375 -1.75 4.109375 -1.8125 C 3.515625 -2.109375 3.5 -2.109375 2.71875 -2.484375 L 4.09375 -3.15625 C 4.25 -3.234375 4.328125 -3.265625 4.328125 -3.421875 C 4.328125 -3.5625 4.203125 -3.703125 4.0625 -3.703125 C 3.984375 -3.703125 3.96875 -3.703125 3.71875 -3.515625 L 2.609375 -2.703125 Z M 2.734375 -4.25 "/>
</symbol>
</g>
</defs>
<g id="surface1">
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-1" x="3.321" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-1" x="9.014" y="7.815"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="15.698" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-1" x="25.66" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-2" x="31.354" y="7.815"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph3-1" x="38.037" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-2" x="48" y="11.43"/>
<use xlink:href="#glyph2-3" x="52.9813" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph3-2" x="60.177" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-1" x="67.372" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph3-1" x="75.28" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-4" x="85.242" y="11.43"/>
<use xlink:href="#glyph2-5" x="90.2233" y="11.43"/>
<use xlink:href="#glyph2-3" x="95.2046" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-1" x="100.186" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph1-2" x="105.88" y="7.815"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="112.563" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-4" x="122.523607" y="11.43"/>
<use xlink:href="#glyph2-6" x="127.504907" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph3-2" x="134.702" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph0-1" x="141.898" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-1" x="149.805" y="11.43"/>
</g>
<g style="fill:rgb(0%,0%,0%);fill-opacity:1;">
<use xlink:href="#glyph2-6" x="159.765607" y="11.43"/>
<use xlink:href="#glyph2-7" x="164.746907" y="11.43"/>
</g>
</g>
</svg>
</center>
Dividing gives the quotient <img class="equation_image" title=" \displaystyle x - 16 " src="/equation_images/%20%5Cdisplaystyle%20x%20-%2016%20" alt="LaTeX: \displaystyle x - 16 " data-equation-content=" \displaystyle x - 16 " /> and the remainder <img class="equation_image" title=" \displaystyle 131 x + 963 " src="/equation_images/%20%5Cdisplaystyle%20131%20x%20%2B%20963%20" alt="LaTeX: \displaystyle 131 x + 963 " data-equation-content=" \displaystyle 131 x + 963 " /> . The oblique asymptote is <img class="equation_image" title=" \displaystyle y = x - 16 " src="/equation_images/%20%5Cdisplaystyle%20y%20%3D%20x%20-%2016%20" alt="LaTeX: \displaystyle y = x - 16 " data-equation-content=" \displaystyle y = x - 16 " /> . </p> </p>