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

1 Answer
Oct 27, 2017

Answer:

#x=1/2color(white)("xxxx")# or #color(white)("xxxx")x=-3#

Explanation:

Given
#color(white)("XXX")2/(x+1)+5/(x-2)=-2#

Multiply everything (on both sides by #(x+1)(x-2)#
#color(white)("XXX")2(x-2)+5(x+1)=-2(x+1)(x-2)#

#color(white)("XXX")2x-4+5x+5=-2x^2+2x+4#

#color(white)("XXX")7x+1=-2x^2+2x+4#

Subtract #(7x+1)# from both sides (and reverse the sides)
#color(white)("XXX")-2x^2-5x+3=0#

Multiply both sides by #(-1)#
#color(white)("XXX")2x^2+5x-3=0#

Factor
#color(white)("XXX")(2x-1)(x+3)=0#

#{:("Either ",2x-1=0," or ",x+3=0),(,rarr x=1/2,,rarr x=-3):}#