Question

simplify.\\(
\frac{16w^{3}x^{3}}{4u^{2}w^{5} + 12w^{5}}
\\)

Explanation:

Step1: Factor denominator's GCF

Factor out $4w^5$ from the denominator:
$4u^2w^5 + 12w^5 = 4w^5(u^2 + 3)$

Step2: Rewrite the original expression

Substitute factored denominator into the fraction:
$\frac{16w^3x^3}{4w^5(u^2 + 3)}$

Step3: Simplify coefficients and exponents

Simplify the numerical part $\frac{16}{4}=4$, and use exponent rule $\frac{w^3}{w^5}=w^{3-5}=w^{-2}=\frac{1}{w^2}$:
$\frac{4x^3}{w^2(u^2 + 3)}$

Answer:

$\frac{4x^3}{w^2(u^2 + 3)}$