How do you solve $2/(x+1) + 5/(x-2)=-2$ ?

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Answer 1 · 2018-08-06T05:36:19

$x=-3 or x=1/2$

Here ,

$2/(x+1)+5/(x-2)=-2$

Combine the fractions :

$(2(x-2)+5(x+1))/((x-2)(x+1))=(-2(x+1)(x-2))/((x+1)(x-2))$

Simplifying we get

$2(x-2)+5(x+1)=-2(x+1)(x-2)$

Using distributive property :

$2x-4+5x+5=-2(x^2-2x+x-2)$

$:.7x+1=-2x^2+2x+4$

$:.2x^2+5x-3=0$

$:.2x^2+6x-x-3=0$

$:.2x(x+3)-1(x+3)=0$

$:.(x+3)(2x-1)=0$

$:.x+3=0 or 2x-1=0$

$:. x=-3 or x=1/2$

How do you solve 2/(x+1) + 5/(x-2)=-22/(x+1) + 5/(x-2)=-2?