SOLUTION: solve and check your answer 2/x-1+1=4/x^2-1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve and check your answer 2/x-1+1=4/x^2-1      Log On


   

Question 774096: solve and check your answer
2/x-1+1=4/x^2-1
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problem is
2%2F%28%28x-1%29%29 + 1 = 4%2F%28%28x%5E2-1%29%29
Factor the 2nd denominator, this will be the common denominator
2%2F%28%28x-1%29%29 + 1 = 4%2F%28%28x-1%29%28x%2B1%29%29
multiply by the common denominator and you have
2(x+1) +(x+1)(x-1) = 4
2x + 2 + x^2 - 1 = 4
combine on the left to form a quadratic equation
x^2 + 2x + 2 - 1 - 4 = 0
x^2 + 2x - 3 = 0
factors to
(x+3)(x-1) = 0
Two solutions
x = 1
x = -3
:
You can check both of these in the original problem, you should note that
x = 1 is not a valid solution, it results in a denominator of 0