Question

simplify the expression completely if possible.
$\frac{x^{2}-5x - 24}{x^{2}-17x + 72}$

Explanation:

Step1: Factor the numerator

We factor $x^{2}-5x - 24$. We need two numbers that multiply to $-24$ and add up to $-5$. These numbers are $-8$ and $3$. So $x^{2}-5x - 24=(x - 8)(x+3)$.

Step2: Factor the denominator

We factor $x^{2}-17x + 72$. We need two numbers that multiply to $72$ and add up to $-17$. These numbers are $-8$ and $-9$. So $x^{2}-17x + 72=(x - 8)(x - 9)$.

Step3: Simplify the fraction

We have $\frac{(x - 8)(x + 3)}{(x - 8)(x - 9)}$. Cancel out the common factor $(x - 8)$ (assuming $x
eq8$). The simplified expression is $\frac{x + 3}{x - 9}$.

Answer:

$\frac{x + 3}{x - 9}$