SOLUTION: 1/(x-1)^2+3/(x^2-1)=5/(x^2-1)

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Question 526735: 1/(x-1)^2+3/(x^2-1)=5/(x^2-1)
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F%28x-1%29%5E2%2B3%2F%28x%5E2-1%29=%285%29%2F%28x%5E2-1%29%29
1%2F%28x-1%29%5E2%2B3%2F%28x-1%29%28x%2B1%29=%285%29%2F%28x-1%29%28x%2B1%29%29
1%2F%28x-1%29%5E2%2B3%2F%28x-1%29%28x%2B1%29-5%2F%28x-1%29%28x%2B1%29=0%29
Taking LCD
%281%28x%2B1%29%2B3%28x-1%29-5%28x-1%29%29%2F%28x-1%29%5E2%28x%2B1%29=0%29
%28x%2B1%2B3x-3-5x%2B5%29%2F%28x-1%29%5E2%28x%2B1%29=0%29
%28x%2B3x-5x%2B1-3%2B5%29%2F%28x-1%29%5E2%28x%2B1%29=0%29
%28-x%2B3%29%2F%28x-1%29%5E2%28x%2B1%29=0%29
%283-x%29%2F%28x-1%29%5E2%28x%2B1%29=0%29
Multiply by %28x-1%29%5E2%28x%2B1%29 both sides


3-x=0%29
3=x%29
x=3%29


Check
=====
1%2F%283-1%29%5E2%2B3%2F%28%283%29%5E2-1%29=%285%29%2F%28%283%29%5E2-1%29%29
1%2F%282%29%5E2%2B3%2F%28%283%29%5E2-1%29=%285%29%2F%28%283%29%5E2-1%29%29
%281%2F4%29%2B%283%2F%289-1%29%29=%285%29%2F%28%289-1%29%29
%281%2F4%29%2B%283%2F8%29=5%2F8%29
Take LCD
%28%281%2A2%29%2B3%29%2F8%29=5%2F8%29
%282%2B3%29%2F8=5%2F8%29
5%2F8=5%2F8%29