Question

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

Answer 1

`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):}`