Question

simplify the expression completely if possible.
$\frac{x^{2}-3x - 4}{x^{2}+6x + 5}$

Explanation:

Step1: Factor the numerator

Factor $x^{2}-3x - 4$. We need two numbers that multiply to $-4$ and add up to $-3$. The numbers are $-4$ and $1$. So $x^{2}-3x - 4=(x - 4)(x+1)$.

Step2: Factor the denominator

Factor $x^{2}+6x + 5$. We need two numbers that multiply to $5$ and add up to $6$. The numbers are $5$ and $1$. So $x^{2}+6x + 5=(x + 5)(x+1)$.

Step3: Simplify the fraction

$\frac{x^{2}-3x - 4}{x^{2}+6x + 5}=\frac{(x - 4)(x + 1)}{(x + 5)(x+1)}$. Cancel out the common factor $(x + 1)$ (assuming $x
eq - 1$). The simplified form is $\frac{x - 4}{x + 5}$.

Answer:

$\frac{x - 4}{x + 5}$