$\frac{x^{2}+11 x+30}{x^{2}+12 x+36} \div \frac{x^{2}+5 x}{x^{2}+2 x-24}$

Question

Quizplus · Accepted Answer

First, factor all the polynomials in the expression. The given expression simplifies as follows:$\frac{(x+6)(x+5)}{(x+6)^2} \div \frac{x(x+5)}{x^2+2x-24}$$\frac{(x+6)(x+5)}{(x+6)^2} \div \frac{x(x+5)}{(x+6)(x-4)}$When you divide fractions, you multiply by the reciprocal of the divisor:$\frac{(x+6)(x+5)}{(x+6)^2} \times \frac{(x+6)(x-4)}{x(x+5)}$Simplify by canceling out common factors:$\frac{x-4}{x}$Thus, the correct answer is D, $\frac{x-4}{x}$.

x2+11x+30x2+12x+36÷x2+5xx2+2x−24\frac{x^{2}+11 x+30}{x^{2}+12 x+36} \div \frac{x^{2}+5 x}{x^{2}+2 x-24}x2+12x+36x2+11x+30​÷x2+2x−24x2+5x​ A) x−4x2+6x\frac{x-4}{x^{2}+6 x}x2+6xx−4​ B) x−4x-4x−4

$\frac{x^{2}+11 x+30}{x^{2}+12 x+36} \div \frac{x^{2}+5 x}{x^{2}+2 x-24}$ A) $\frac{x-4}{x^{2}+6 x}$ B) $x-4$