Divide and simplify.
-$\frac{x^{2}-64}{x} \div \frac{3 x+24}{x-8}$
A) $\frac{3(x+8)^{2}}{x}$
B) $\frac{3 x}{(x-8)^{2}}$
C) $\frac{(x-8)^{2}}{x}$
D) $\frac{(x-8)^{2}}{3 x}$

Question

Quizplus · Accepted Answer

To divide fractions, multiply by the reciprocal. The expression becomes $\frac{x^{2}-64}{x} \times \frac{x-8}{3x+24}$. Factor $x^{2}-64$ as $(x-8)(x+8)$ and $3x+24$ as $3(x+8)$. The expression simplifies to $\frac{(x-8)(x+8)}{x} \times \frac{x-8}{3(x+8)}$, which simplifies to $\frac{(x-8)^{2}}{3x}$.

Divide and Simplify x2−64x÷3x+24x−8\frac{x^{2}-64}{x} \div \frac{3 x+24}{x-8}xx2−64​÷x−83x+24​ A) 3(x+8)2x\frac{3(x+8)^{2}}{x}x3(x+8)2​ B) 3x(x−8)2\frac{3 x}{(x-8)^{2}}(x−8)23x​ C) (x−8)2x\frac{(x-8)^{2}}{x}x(x−8)2​

Divide and Simplify $\frac{x^{2}-64}{x} \div \frac{3 x+24}{x-8}$ A) $\frac{3(x+8)^{2}}{x}$ B) $\frac{3 x}{(x-8)^{2}}$ C) $\frac{(x-8)^{2}}{x}$