Question

simplify.
\\(\frac{x^2 - 2x - 15}{4x^2 - 12x - 40}\\)

Explanation:

Step1: Factor numerator quadratic

Find two numbers that multiply to $-15$ and add to $-2$; these are $-5$ and $3$.
$x^2 - 2x - 15 = (x - 5)(x + 3)$

Step2: Factor denominator quadratic

First factor out the GCF of 4, then factor the remaining quadratic.
$4x^2 - 12x - 40 = 4(x^2 - 3x - 10)$
Find two numbers that multiply to $-10$ and add to $-3$; these are $-5$ and $2$.
$4(x^2 - 3x - 10) = 4(x - 5)(x + 2)$

Step3: Cancel common factors

Cancel the shared $(x - 5)$ term (where $x
eq 5$).
$\frac{(x - 5)(x + 3)}{4(x - 5)(x + 2)} = \frac{x + 3}{4(x + 2)}$

Answer:

$\frac{x + 3}{4(x + 2)}$ (where $x
eq 5, -2$)