How do you solve $(x-2)/(x+5) - 4/(x+1) = 1/(x+1)$ ?

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Answer 1 · 2018-03-17T03:04:58

$x=9$ or $x=-3$

First, lets rewrite the equation in the form

$(x-2)/(x+5) - 5/(x+1) = 0$

Then we multiply both sides of the equation by $(x+5)(x+1)$ to get rid of the denominators.

This changes the equation to

$(x-2)(x+1)-5(x+5)=0 implies$
$(x^2-x-2)-(5x+25)=0 implies$
$x^2-6x-27=0 implies$
$x^2-9x+3x-27=0 implies$
$x(x-9)+3(x-9)=0 implies$
$(x-9)(x+3)=0$

Thus, either $x=9$ or $x=-3$

How do you solve (x-2)/(x+5) - 4/(x+1) = 1/(x+1)(x-2)/(x+5) - 4/(x+1) = 1/(x+1)?