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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle \frac{6}{x - 1}=\frac{1}{x + 7}\).
The LCD is \(\displaystyle \left(x - 1\right) \left(x + 7\right)\). Multiplying by the LCD to clear the fractions gives \(\displaystyle 6 x + 42 = x - 1\). Isloating \(\displaystyle x\) gives \(\displaystyle x = - \frac{43}{5}\).
\begin{question}Solve $\frac{6}{x - 1}=\frac{1}{x + 7}$.
\soln{9cm}{The LCD is $\left(x - 1\right) \left(x + 7\right)$. Multiplying by the LCD to clear the fractions gives $6 x + 42 = x - 1$. Isloating $x$ gives $x = - \frac{43}{5}$. }
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Solve <img class="equation_image" title=" \displaystyle \frac{6}{x - 1}=\frac{1}{x + 7} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B6%7D%7Bx%20-%201%7D%3D%5Cfrac%7B1%7D%7Bx%20%2B%207%7D%20" alt="LaTeX: \displaystyle \frac{6}{x - 1}=\frac{1}{x + 7} " data-equation-content=" \displaystyle \frac{6}{x - 1}=\frac{1}{x + 7} " /> .</p> </p><p> <p>The LCD is <img class="equation_image" title=" \displaystyle \left(x - 1\right) \left(x + 7\right) " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28x%20-%201%5Cright%29%20%5Cleft%28x%20%2B%207%5Cright%29%20" alt="LaTeX: \displaystyle \left(x - 1\right) \left(x + 7\right) " data-equation-content=" \displaystyle \left(x - 1\right) \left(x + 7\right) " /> . Multiplying by the LCD to clear the fractions gives <img class="equation_image" title=" \displaystyle 6 x + 42 = x - 1 " src="/equation_images/%20%5Cdisplaystyle%206%20x%20%2B%2042%20%3D%20x%20-%201%20" alt="LaTeX: \displaystyle 6 x + 42 = x - 1 " data-equation-content=" \displaystyle 6 x + 42 = x - 1 " /> . Isloating <img class="equation_image" title=" \displaystyle x " src="/equation_images/%20%5Cdisplaystyle%20x%20" alt="LaTeX: \displaystyle x " data-equation-content=" \displaystyle x " /> gives <img class="equation_image" title=" \displaystyle x = - \frac{43}{5} " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20-%20%5Cfrac%7B43%7D%7B5%7D%20" alt="LaTeX: \displaystyle x = - \frac{43}{5} " data-equation-content=" \displaystyle x = - \frac{43}{5} " /> . </p> </p>