Question

`1/(x+1)+2/(x+2)=5/(x+4),x≠-1,-2,-4`

Answer 1

`1/(x+1)+2/(x+2)=5/(x+4),x≠-1,-2,-4` 

⇒`(x+2+2x+2)/((x+1)(x+2))=5/(x+4)` 

⇒`(3x+4)/(x^2+3x+2)=5/(x+4)` 

⇒`(3x+4) (x+4)=5(x^2+3x+2)` 

⇒`3x^2+16x+16=5x^2+15x+10` 

⇒`2x^2-x-6=0` 

⇒`2x^2-4x-3x-6=0` 

⇒`2x(x-2)+3(x-2)=0` 

⇒`(x-2)(2x+3)=0` 

⇒`3x^2+16x+16=5x^2+15x+10` 

⇒`2x^2-x-6=0` 

⇒`2x^2-4x+3x-6=0` 

⇒`2x(x-2)+3(x-2)=0` 

⇒`(x-2) (2x+3)=0` 

⇒`x-2=0  or  2x+3=0` 

⇒`x=2  or  x=-3/2` 

Hence, 2 and  `-3/2` are the roots of the given equation.