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) $\frac{7 x}{4 (x + 1)}$

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Answer

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

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: $\frac{2 x^{2}}{x + 3}$

5) 2x3+6x2x2−x−20÷x2+6x+9x2−x−20A) 2x2x+3B) 6x+6C) 352D) 7x4(x+1)

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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) $\frac{7 x}{4 (x + 1)}$