SOLUTION: How would I solve this rational equation: (x+5/x^2+x) = (1/x^2+x) - (x-6/x+1)

Algebra ->  Rational-functions -> SOLUTION: How would I solve this rational equation: (x+5/x^2+x) = (1/x^2+x) - (x-6/x+1)      Log On


   

Question 1016539: How would I solve this rational equation: (x+5/x^2+x) = (1/x^2+x) - (x-6/x+1)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B5%29%2F%28x%5E2%2Bx%29 = 1%2F%28x%5E2%2Bx%29 - %28x-6%29%2F%28x%2B1%29
Factor out x
%28x%2B5%29%2F%28x%28x%2B1%29%29 = 1%2F%28x%28x%2B1%29%29 - %28x-6%29%2F%28x%2B1%29
multiply each by x(x+1), cancel the denominators and you have
(x+5) = 1 - x(x-6)
x + 5 = 1 - x^2 + 6x
Combine like terms on the left
x^2 + x - 6x + 5 - 1 = 0
x^2 - 5x + 4 = 0
Factors to
(x-4)(x-1) = 0
Two solutions
x = 4
and
x = 1
:
I'll let you check both solutions in the original equation