20 Simplify each of the following.
(a) $\frac{4 x^{2}}{18 (x - 3)^{2}} \times \frac{15 (x - 3)}{12 x^{4}}$
(b) $\frac{(x + 6)}{(x + 2)^{2} (x + 3)} \div \frac{4}{(x + 2) (x + 3)}$

Answer

Expert–verified

Hide Steps

Answer

$Final Answer:$ (a) $\frac{5}{18 x^{2} (x - 3)}$ (b) $\frac{x + 6}{4 (x + 2)}$

Steps

Step 1 ：Simplify expression (a): $\frac{4 x^{2}}{18 (x - 3)^{2}} \times \frac{15 (x - 3)}{12 x^{4}}$ to $\frac{5}{18 x^{2} (x - 3)}$

Step 2 ：Simplify expression (b): $\frac{(x + 6)}{(x + 2)^{2} (x + 3)} \div \frac{4}{(x + 2) (x + 3)}$ to $\frac{x + 6}{4 (x + 2)}$

Step 3 ： $Final Answer:$ (a) $\frac{5}{18 x^{2} (x - 3)}$ (b) $\frac{x + 6}{4 (x + 2)}$