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Questions: Algebra BusinessCalculus
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Solve \(\displaystyle \frac{5}{x + 3}=\frac{4}{x - 5}\).
The LCD is \(\displaystyle \left(x - 5\right) \left(x + 3\right)\). Multiplying by the LCD to clear the fractions gives \(\displaystyle 5 x - 25 = 4 x + 12\). Isloating \(\displaystyle x\) gives \(\displaystyle x = 37\).
\begin{question}Solve $\frac{5}{x + 3}=\frac{4}{x - 5}$.
\soln{9cm}{The LCD is $\left(x - 5\right) \left(x + 3\right)$. Multiplying by the LCD to clear the fractions gives $5 x - 25 = 4 x + 12$. Isloating $x$ gives $x = 37$. }
\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{5}{x + 3}=\frac{4}{x - 5} " src="/equation_images/%20%5Cdisplaystyle%20%5Cfrac%7B5%7D%7Bx%20%2B%203%7D%3D%5Cfrac%7B4%7D%7Bx%20-%205%7D%20" alt="LaTeX: \displaystyle \frac{5}{x + 3}=\frac{4}{x - 5} " data-equation-content=" \displaystyle \frac{5}{x + 3}=\frac{4}{x - 5} " /> .</p> </p><p> <p>The LCD is <img class="equation_image" title=" \displaystyle \left(x - 5\right) \left(x + 3\right) " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28x%20-%205%5Cright%29%20%5Cleft%28x%20%2B%203%5Cright%29%20" alt="LaTeX: \displaystyle \left(x - 5\right) \left(x + 3\right) " data-equation-content=" \displaystyle \left(x - 5\right) \left(x + 3\right) " /> . Multiplying by the LCD to clear the fractions gives <img class="equation_image" title=" \displaystyle 5 x - 25 = 4 x + 12 " src="/equation_images/%20%5Cdisplaystyle%205%20x%20-%2025%20%3D%204%20x%20%2B%2012%20" alt="LaTeX: \displaystyle 5 x - 25 = 4 x + 12 " data-equation-content=" \displaystyle 5 x - 25 = 4 x + 12 " /> . 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 = 37 " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%2037%20" alt="LaTeX: \displaystyle x = 37 " data-equation-content=" \displaystyle x = 37 " /> . </p> </p>