Question

exam 1 fall25
due sunday by 11:59pm points 100 submitting an external tool available until sep 21
exam 1 fall25
score: 15/100 answered: 6/18
question 7
simplify:
\\(\frac{5 - \frac{9}{x + 3}}{\frac{8x}{x + 3}-2}\\)

Explanation:

Step1: Simplify numerator

First, find a common - denominator for the numerator $5-\frac{9}{x + 3}$. The common denominator is $x + 3$. So, $5=\frac{5(x + 3)}{x+3}=\frac{5x+15}{x + 3}$. Then $5-\frac{9}{x + 3}=\frac{5x + 15-9}{x + 3}=\frac{5x+6}{x + 3}$.

Step2: Simplify denominator

For the denominator $\frac{8x}{x + 3}-2$, find a common - denominator. Since $2=\frac{2(x + 3)}{x + 3}=\frac{2x+6}{x + 3}$, then $\frac{8x}{x + 3}-2=\frac{8x-(2x + 6)}{x + 3}=\frac{8x-2x-6}{x + 3}=\frac{6x-6}{x + 3}$.

Step3: Divide the simplified numerator by the simplified denominator

We have $\frac{\frac{5x + 6}{x + 3}}{\frac{6x-6}{x + 3}}$. When dividing by a fraction, we multiply by its reciprocal, so $\frac{5x + 6}{x + 3}\times\frac{x + 3}{6x-6}=\frac{5x + 6}{6x-6}$, where $x
eq - 3$.

Answer:

$\frac{5x + 6}{6x-6}$