Question 239853
Solve {{{(x+5)/(x^2+x) = 1/(x^2+x) - (x-6)/(x+1)}}}<br>

First we need to factor the denominator of the above problem.  <br>

{{{(x+5)/(x^2+x) = 1/(x^2+x) - (x-6)/(x+1)}}}
= {{{(x+5)/(x(x+1)) = 1/(x(x+1)) - (x-6)/(x+1)}}}<br>

Now we find a common denominator.  It will be x(x+1).  Now multiply the origonal equation by x(x+1) and simplify.<br>

{{{(x+5)/(x(x+1)) = 1/(x(x+1)) - (x-6)/(x+1)}}}<br>

{{{(x+5)(x)(x+1)/(x(x+1)) = 1(x)(x+1)/(x(x+1)) - (x)(x+1)(x-6)/(x+1)}}}
{{{x+5 = 1 - (x)(x-6)}}}<br>

Now we solve for x.
x+5 = 1 - (x)(x-6)
x+5 = 1 - x^2+6x
x^2-6x+x+5-1 = 0
x^2-5x+4 = 0
(x-4)(x-1) = 0
x = 4 and x = 1