Question

simplify.

\\\frac{27 - 3y^2}{y^2 - 6y + 9}\\

Explanation:

Factor the numerator

$$ 27 - 3y^2 = 3(9 - y^2) = 3(3 - y)(3 + y) $$

Factor the denominator

$$ y^2 - 6y + 9 = (y - 3)^2 = (3 - y)^2 $$

Simplify the rational expression

$$ \frac{3(3 - y)(3 + y)}{(3 - y)^2} = \frac{3(3 + y)}{3 - y} \quad (y eq 3) $$

Answer:

$$ \frac{3(3 + y)}{3 - y} $$