$\frac{x^{2}-10 x+21}{x^{2}+14 x+49} \div \frac{x^{2}-6 x+9}{x^{2}-2 x-35}$

A) $-\frac{x+5}{x-3}$

B) $\frac{(x-7)^{2}(x+5)}{(x+7)^{2}(x-3)}$

C) $\frac{(x-7)^{2}(x+5)}{(x+7)^{2}}$

D) $\frac{(x-3)^{3}}{(x+7)^{2}(x+5)}$

Question

$\frac{x^{2}-10 x+21}{x^{2}+14 x+49} \div \frac{x^{2}-6 x+9}{x^{2}-2 x-35}$

A) $-\frac{x+5}{x-3}$

B) $\frac{(x-7)^{2}(x+5)}{(x+7)^{2}(x-3)}$

C) $\frac{(x-7)^{2}(x+5)}{(x+7)^{2}}$

D) $\frac{(x-3)^{3}}{(x+7)^{2}(x+5)}$

Quizplus · Accepted Answer

The given expression simplifies as follows: Factorize the numerators and denominators of both fractions. The first fraction becomes $\frac{(x-7)(x-3)}{(x+7)^2}$, and the second fraction becomes $\frac{(x-3)^2}{(x-7)(x+5)}$. When dividing fractions, multiply the first fraction by the reciprocal of the second, resulting in $\frac{(x-7)(x-3)}{(x+7)^2} \cdot \frac{(x-7)(x+5)}{(x-3)^2}$. Simplify by canceling out $(x-3)$ from the numerator and denominator, leaving $\frac{(x-7)^2(x+5)}{(x+7)^2}$.