Question

Find x in given equation:

1/(x + 1) + 2/(x + 2) = 5/(x + 4)

Answer 1

Solution:

Given:

$\sf{\implies \dfrac{1}{x+1}+\dfrac{2}{x+2}=\dfrac{5}{x+4}}$

To find:

=> Value of x.

So,

$\sf{\implies \dfrac{1}{x+1}+\dfrac{2}{x+2}=\dfrac{5}{x+4}}$

First we will take LCM,

$\sf{\implies \dfrac{x+2+2x+2}{x^{2}+3x+2}=\dfrac{5}{x+4}}$

Then cross multiply,

$\sf{\implies (x+4)(x+2+2x+2)=5(x^{2}+3x+2)}$

$\sf{\implies x^{2}+2x+2x^{2}+2x+4x+8+8x+8=5x^{2}+15x+10}$

$\sf{\implies 3x^{2}+16x+16=5x^{2}+15x+10}$

$\sf{\implies 3x^{2}+16x+16-5x^{2}-15x-10=0}$

$\sf{\implies -2x^{2}+x+6=0}$

By splitting middle term method,

$\sf{\implies -2x^{2}+x+6=0}$

$\sf{\implies -2x^{2}+4x-3x+6}$

$\sf{\implies -2x(x+2)-3(x+2)}$

$\sf{\implies (-2x-3) (x+2)}$

So,

$\sf{\implies -2x-3=0}$

$\sf{\implies -2x = 3}$

${\boxed{\boxed{\bf{\implies x = -\dfrac{3}{2}}}}}$

$\sf{\implies x+2=0}$

${\boxed{\boxed{\bf{\implies x = -2}}}}}$