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#