SOLUTION: Hi, I am doing well but am stuck on this problem (after 45 minutes and 3 different answers) - {x/{x²-1)}-{(x+3)/(x²-x)}=-3/(x²+x) The book says the answer is (-6), but I don't see

Algebra ->  Algebra  -> Graphs -> SOLUTION: Hi, I am doing well but am stuck on this problem (after 45 minutes and 3 different answers) - {x/{x²-1)}-{(x+3)/(x²-x)}=-3/(x²+x) The book says the answer is (-6), but I don't see       Log On

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Question 10105: Hi, I am doing well but am stuck on this problem (after 45 minutes and 3 different answers) - {x/{x²-1)}-{(x+3)/(x²-x)}=-3/(x²+x) The book says the answer is (-6), but I don't see how. Thanks in advance for your help!
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Right, well first off, get rid of the fractions. To do this, we need to find common factors, so factorise the denominators first...

%28x%2F%28%28x%2B1%29%28x-1%29%29%29+-+%28%28x%2B3%29%2F%28%28x%29%28x-1%29%29%29+=+-3%2F%28x%28x%2B1%29%29

ok, so we will mutliply all 3 terms by x(x+1)(x-1), to leave:

x%5E2+-+%28x%2B1%29%28x%2B3%29+=+-3%28x-1%29
x%5E2+-+%28x%5E2%2B4x%2B3%29+=+-3x%2B3
x%5E2+-+x%5E2+-+4x+-+3+=+-3x+%2B+3
-4x - 3 = -3x + 3
-x - 3 = 3
-x = 6

--> x = -6

jon