Question

question
simplify the expression completely if possible.
$\frac{x^{2}+6x-16}{2x^{2}-4x}$

Explanation:

Step1: Factor numerator

Find two numbers that multiply to $-16$ and add to $6$: $8$ and $-2$.
$x^2 + 6x - 16 = (x + 8)(x - 2)$

Step2: Factor denominator

Factor out the greatest common factor $2x$.
$2x^2 - 4x = 2x(x - 2)$

Step3: Cancel common factors

Cancel $(x - 2)$ from numerator and denominator (where $x
eq 2, 0$).
$\frac{(x + 8)(x - 2)}{2x(x - 2)} = \frac{x + 8}{2x}$

Answer:

$\frac{x + 8}{2x}$ (where $x
eq 0, 2$)