Question

simplify.\\(
\frac{27u^{2}(u + 3)^{4}(3u - 5)}{18u^{4}(u + 3)^{5}}
\\)you may leave the numerator and denominator of your answer in factored form.

Explanation:

Step1: Simplify constant coefficients

$\frac{27}{18} = \frac{3}{2}$

Step2: Simplify $u$ terms

$\frac{u^2}{u^4} = \frac{1}{u^{4-2}} = \frac{1}{u^2}$

Step3: Simplify $(u+3)$ terms

$\frac{(u+3)^4}{(u+3)^5} = \frac{1}{(u+3)^{5-4}} = \frac{1}{u+3}$

Step4: Combine remaining factors

Multiply the simplified parts together, keeping the $(3u-5)$ term in the numerator.

Answer:

$\frac{3(3u-5)}{2u^2(u+3)}$