Question

simplify.

\\\frac{96 - 6v^2}{v^2 - 11v + 28}\\

Explanation:

Factor the numerator

$$ 96 - 6v^2 = 6(16 - v^2) = 6(4 - v)(4 + v) $$

Factor the denominator

$$ v^2 - 11v + 28 = (v - 7)(v - 4) $$

Simplify the rational expression

$$ \frac{6(4 - v)(4 + v)}{(v - 7)(v - 4)} = \frac{-6(v - 4)(v + 4)}{(v - 7)(v - 4)} = \frac{-6(v + 4)}{v - 7} = \frac{-6v - 24}{v - 7} $$

Answer:

$$\frac{-6(v + 4)}{v - 7}$$