Question

question
simplify the expression completely if possible.
$\frac{x^{2}-2x-48}{x^{2}-17x+72}$

Explanation:

Step1: Factor numerator

Find two numbers that multiply to $-48$ and add to $-2$. These numbers are $-8$ and $6$.
$x^2 - 2x - 48 = (x - 8)(x + 6)$

Step2: Factor denominator

Find two numbers that multiply to $72$ and add to $-17$. These numbers are $-8$ and $-9$.
$x^2 - 17x + 72 = (x - 8)(x - 9)$

Step3: Cancel common factors

Cancel the $(x - 8)$ term (where $x
eq 8$ to avoid division by zero).
$\frac{(x - 8)(x + 6)}{(x - 8)(x - 9)} = \frac{x + 6}{x - 9}$

Answer:

$\frac{x + 6}{x - 9}$ (where $x
eq 8, 9$)