$\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}$

A) $x+2$

B) $\frac{x+2}{x}$

C) $\frac{x+2}{x^{2}+7 x}$

D) $\frac{x}{x^{2}+11 x+28}$

Question

$\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}$

A) $x+2$

B) $\frac{x+2}{x}$

C) $\frac{x+2}{x^{2}+7 x}$

D) $\frac{x}{x^{2}+11 x+28}$

Quizplus · Accepted Answer

First, factorize all the quadratic expressions: $\frac{(x+4)^2}{(x+4)(x+7)} \div \frac{x(x+4)}{(x+2)(x+7)}$. Simplify by dividing the numerators and denominators, which gives $\frac{x+2}{x}$.

x2+8x+16x2+11x+28÷x2+4xx2+9x+14\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}x2+11x+28x2+8x+16​÷x2+9x+14x2+4x​ A) x+2x+2x+2 B) x+2x\frac{x+2}{x}xx+2​ C) x+2x2+7x\frac{x+2}{x^{2}+7 x}x2+7xx+2​

$\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}$ A) $x+2$ B) $\frac{x+2}{x}$ C) $\frac{x+2}{x^{2}+7 x}$