5) $\frac{2 x^{3}+6 x^{2}}{x^{2}-x-20} \div \frac{x^{2}+6 x+9}{x^{2}-x-20}$
A) $\frac{2 x^{2}}{x+3}$
B) $\frac{6}{x+6}$
C) $\frac{35}{2}$
D) $\frac{7 x}{4(x+1)}$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $\boxed{\frac{2 x^{2}}{x+3}}$

Steps

Step 1 ：Rewrite the division as multiplication by the reciprocal: $\frac{2 x^{3}+6 x^{2}}{x^{2}-x-20} \times \frac{x^{2}-x-20}{x^{2}+6 x+9}$

Step 2 ：Simplify the expression by canceling out common factors: $\frac{2 x^{2}(x+3)}{x+3}$

Step 3 ：Final Answer: $\boxed{\frac{2 x^{2}}{x+3}}$