Question

rewrite as equivalent rational expressions with denominator \\(2(w + 3)^2(w - 1)\\):

\\\frac{9}{2w^2 + 12w + 18}, \frac{4w}{2w^2 + 4w - 6}\\

Explanation:

Factor the first denominator

Using the Greatest Common Factor Factoring and Perfect Square Trinomials knowledge points

$$
LATEXBLOCK0
$$

Factor the second denominator

Using the Greatest Common Factor Factoring and Trinomial Factorization knowledge points

$$
LATEXBLOCK1
$$

Convert the first rational expression

Using the Equivalent Rational Expressions knowledge point

$$
LATEXBLOCK2
$$

Convert the second rational expression

Using the Equivalent Rational Expressions knowledge point

$$
LATEXBLOCK3
$$

Answer:

$$\frac{9w - 9}{2(w + 3)^2(w - 1)}, \frac{4w^2 + 12w}{2(w + 3)^2(w - 1)}$$