SOLUTION: Can you show me the STEPS to solve the following: 1 over x-1 + 4 over x^2-1 - 2 over x^2-2x+1. Thanks.

Algebra ->  Equations -> SOLUTION: Can you show me the STEPS to solve the following: 1 over x-1 + 4 over x^2-1 - 2 over x^2-2x+1. Thanks.      Log On


   

Question 464266: Can you show me the STEPS to solve the following: 1 over x-1 + 4 over x^2-1 - 2 over x^2-2x+1. Thanks.
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
To solve the equation 1%2F%28x-1%29%2B4%2F%28x%5E2-1%29=%28-2%29%2F%28x%5E2-2x%2B1%29, first we factor the
denominators to find the LCD.1%2F%28x-1%29%2B4%2F%28x-1%29%28x%2B1%29=%28-2%29%2F%28x-1%29%5E2. the LCD is
%28x-1%29%5E2%28x%2B1%29. Second write all terms with the same denominator:

Multiply both sides by LCD, and cancel like terms:
x%5E2-1%2B4%28x-1%29=-2%28x%2B1%29, set the equation equal to zero:x%5E2-2x-3=0
Solve this equation by factoring:%28x%2B1%29%28x-3%29=0 The solution is:
x+1=0 <=> x=-1, and x-3=0 <=> x=3. Reject the solution x=-1 because the equation is undefined and the only solution is x=3.