Question

Solve for x :

`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`

Answer 1

`2/(x+1)+3/(2(x-2))=23/(5x)`

`=>(4(x-2)+3(x+1))/(2(x+1)(x-2))=23/(5x)`

`=>(7x-5)/(2(x^2-x-2))=23/(5x)`

 ⇒5x(7x−5)=46(x²−x−2)

⇒11x²−21x−92=0

⇒11x²−44x+23x−92=0

⇒11x(x−4)+23(x−4)=0

⇒(11x+23)(x−4)=0

`=>x = -23/11,4`