which multiplication expression is equivalent to $\frac{x + 8}{x^{2}}div\frac{2x + 16}{2x^{2}}$?\n$\frac{x^{2…

which multiplication expression is equivalent to $\frac{x + 8}{x^{2}}div\frac{2x + 16}{2x^{2}}$?\n$\frac{x^{2}}{x + 8}cdot\frac{2x^{2}}{2x + 16}$\n$\frac{x + 8}{x^{2}}cdot\frac{2x + 16}{2x^{2}}$\n$\frac{x + 8}{x^{2}}cdot\frac{2x^{2}}{2x + 16}$

which multiplication expression is equivalent to $\frac{x + 8}{x^{2}}div\frac{2x + 16}{2x^{2}}$?\n$\frac{x^{2}}{x + 8}cdot\frac{2x^{2}}{2x + 16}$\n$\frac{x + 8}{x^{2}}cdot\frac{2x + 16}{2x^{2}}$\n$\frac{x + 8}{x^{2}}cdot\frac{2x^{2}}{2x + 16}$

Answer

Explanation:

Step1: Recall division - to - multiplication rule

Dividing by a fraction is the same as multiplying by its reciprocal. Given $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$. For the expression $\frac{x + 8}{x^{2}}\div\frac{2x+16}{2x^{2}}$, the reciprocal of $\frac{2x + 16}{2x^{2}}$ is $\frac{2x^{2}}{2x+16}$.

Step2: Rewrite the division as multiplication

So, $\frac{x + 8}{x^{2}}\div\frac{2x+16}{2x^{2}}=\frac{x + 8}{x^{2}}\times\frac{2x^{2}}{2x+16}$.

Answer:

$\frac{x + 8}{x^{2}}\cdot\frac{2x^{2}}{2x + 16}$ (the third option)