Question

question
simplify the expression completely if possible.
$\frac{x^{2}+13x+42}{x^{2}-49}$

Explanation:

Step1: Factor numerator

Find two numbers that multiply to 42 and add to 13.
$x^2 + 13x + 42 = (x+6)(x+7)$

Step2: Factor denominator

Use difference of squares: $a^2-b^2=(a-b)(a+b)$.
$x^2 - 49 = (x-7)(x+7)$

Step3: Cancel common factors

Eliminate the shared $(x+7)$ term, $x
eq-7$.
$\frac{(x+6)(x+7)}{(x-7)(x+7)} = \frac{x+6}{x-7}$

Answer:

$\frac{x+6}{x-7}$ (where $x
eq -7, 7$)