$\frac{x^{2}+5 x+4}{x^{2}+10 x+24} \cdot \frac{x^{2}-11 x+30}{x^{2}-4 x-5}$

A) -1

B) $\frac{x-6}{x+6}$

C) $\frac{x+6}{x-6}$

D) 1

Question

$\frac{x^{2}+5 x+4}{x^{2}+10 x+24} \cdot \frac{x^{2}-11 x+30}{x^{2}-4 x-5}$

A) -1

B) $\frac{x-6}{x+6}$

C) $\frac{x+6}{x-6}$

D) 1

Quizplus · Accepted Answer

To simplify the given expression, factor each quadratic polynomial:$\frac{x^{2}+5 x+4}{x^{2}+10 x+24} \cdot \frac{x^{2}-11 x+30}{x^{2}-4 x-5}$= $\frac{(x+4)(x+1)}{(x+6)(x+4)} \cdot \frac{(x-6)(x-5)}{(x-5)(x+1)}$Cancel out the common factors $(x+4), (x+1),$ and $(x-5)$ from the numerator and denominator:= $\frac{x-6}{x+6}$Thus, the simplified form is $\frac{x-6}{x+6}$, which corresponds to choice B.

x2+5x+4x2+10x+24⋅x2−11x+30x2−4x−5\frac{x^{2}+5 x+4}{x^{2}+10 x+24} \cdot \frac{x^{2}-11 x+30}{x^{2}-4 x-5}x2+10x+24x2+5x+4​⋅x2−4x−5x2−11x+30​ A) -1 B)

$\frac{x^{2}+5 x+4}{x^{2}+10 x+24} \cdot \frac{x^{2}-11 x+30}{x^{2}-4 x-5}$ A) -1

B)