Question

Find the product of
x2 + x - 12/ x2-5x - 6 and x2 + 6x + 5/ x2 + 7x + 12​

Answer 1

Answer:

(x-3)(x+5)/(x-6)(x+3)

Answer 2

$\underline{\textsf{To find:}}$

$\textsf{The product of}$

$\mathsf{\dfrac{x^2+x-12}{x^2-5x-6}\;and\;\dfrac{x^2+6x+5}{x^2+7x+12}}$

$\underline{\textsf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{\dfrac{x^2+x-12}{x^2-5x-6}{\times}\dfrac{x^2+6x+5}{x^2+7x+12}}$

$\textsf{First we factorize all the polynomials}$

$\left\begin{array}{rl}x^2+x-12&=x^2+4x-3x-12\\&\\&=x(x+4)-3(x+4)\\&\\&=(x-3)(x+4)\end{array}}$

$\left\begin{array}{rl}x^2-5x-6&=x^2-6x+x-6\\&\\&=x(x-6)+1(x-6)\\&\\&=(x-6)(x+1)\end{array}}$

$\left\begin{array}{rl}x^2+6x+5&=x^2+5x+x+5\\&\\&=x(x+5)+1(x+5)\\&\\&=(x+5)(x+1)\end{array}}$

$\left\begin{array}{rl}x^2+7x+12&=x^2+4x+3x+12\\&\\&=x(x+4)+3(x+4)\\&\\&=(x+4)(x+3)\end{array}}$

$\mathsf{=\dfrac{(x-3)(x+4)}{(x-6)(x+1)}{\times}\dfrac{(x+5)(x+1)}{(x+4)(x+3)}}$

$\mathsf{=\dfrac{(x-3)}{(x-6)}{\times}\dfrac{(x+5)}{(x+3)}}$

$\mathsf{=\dfrac{(x-3)(x+5)}{(x-6)(x+3)}}$

$\mathsf{=\dfrac{x^2+2x-15}{x^2-3x-18}}$

$\underline{\textsf{Answer:}}$

$\mathsf{The\;product\;is\;\dfrac{x^2+2x-15}{x^2-3x-18}}$