SOLUTION: I am supposed to solve this rational equation. x/x+1 + 5/x-1=1 (x over x+1 plus 5 over x-1 equals 1). I know i need to find the least common denominator. i think that is (x+1)(x-1)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am supposed to solve this rational equation. x/x+1 + 5/x-1=1 (x over x+1 plus 5 over x-1 equals 1). I know i need to find the least common denominator. i think that is (x+1)(x-1)      Log On


   

Question 452345: I am supposed to solve this rational equation. x/x+1 + 5/x-1=1 (x over x+1 plus 5 over x-1 equals 1). I know i need to find the least common denominator. i think that is (x+1)(x-1). My biggest problem is knowing what to do with the numerator. Thanks and please help!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve this rational equation. x%2F%28x%2B1%29+%2B+5%2F%28x-1%29 = 1
:
Multiply each term by (x+1)(x-1)
:
(x+1)(x-1)*x%2F%28x%2B1%29 + (x-1)(x+1)*5%2F%28x-1%29 = (x-1)(x+1)*1
:
Cancel the denominators and you are left with
(x-1)*x + (x+1)*5 = (x+1)(x-1)
then
x^2 - x + 5x + 5 = x^2 - x + x - 1
x^2 + 4x + 5 = x^2 - 1
Combine the x^2 on the left, number on the right
x^2 - x^2 + 4x = - 1 - 5
4x = -6
x = %28-6%29%2F4
x = -1.5
:
:
see if that works in the original problem
%28-1.5%29%2F%28-1.5%2B1%29+%2B+5%2F%28-1.5-1%29 = 1
%28-1.5%29%2F%28-.5%29+%2B+5%2F%28-2.5%29 = 1
+3 - 2 = 1