Divide and simplify.
-$\frac{x^{2}-16}{x} \div \frac{5 x+20}{x-4}$
A) $\frac{5 x}{(x-4)^{2}}$
B) $\frac{(\mathrm{x}-4)^{2}}{\mathrm{x}}$
C) $\frac{5(x+4)^{2}}{x}$
D) $\frac{(x-4)^{2}}{5 x}$

Question

Quizplus · Accepted Answer

First, rewrite the division as multiplication by the reciprocal: $\frac{x^{2}-16}{x} \times \frac{x-4}{5x+20}$. Factor the expressions: $x^2-16 = (x-4)(x+4)$ and $5x+20 = 5(x+4)$. The expression becomes $\frac{(x-4)(x+4)}{x} \times \frac{x-4}{5(x+4)}$. Cancel out the common terms $(x+4)$, resulting in $\frac{(x-4)^2}{5x}$.

Divide and Simplify x2−16x÷5x+20x−4\frac{x^{2}-16}{x} \div \frac{5 x+20}{x-4}xx2−16​÷x−45x+20​ A) 5x(x−4)2\frac{5 x}{(x-4)^{2}}(x−4)25x​ B) (x−4)2x\frac{(\mathrm{x}-4)^{2}}{\mathrm{x}}x(x−4)2​ C) 5(x+4)2x\frac{5(x+4)^{2}}{x}x5(x+4)2​

Divide and Simplify $\frac{x^{2}-16}{x} \div \frac{5 x+20}{x-4}$ A) $\frac{5 x}{(x-4)^{2}}$ B) $\frac{(\mathrm{x}-4)^{2}}{\mathrm{x}}$ C) $\frac{5(x+4)^{2}}{x}$