SOLUTION: 2x+3/x-1=10/X^2-1+2x-3/x+1 how do you solve this problem? thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 2x+3/x-1=10/X^2-1+2x-3/x+1 how do you solve this problem? thanks      Log On


   

Question 381559: 2x+3/x-1=10/X^2-1+2x-3/x+1 how do you solve this problem? thanks
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the common denominator, x%5E2-1=%28x%2B1%29%28x-1%29
%282x%2B3%29%2F%28x-1%29=10%2F%28x%5E2-1%29%2B%282x-3%29%2F%28x%2B1%29

%28%282x%2B3%29%28x%2B1%29-10-%282x-3%29%28x-1%29%29%2F%28%28x-1%29%28x%2B1%29%29=0
%282x%5E2%2B5x%2B3-10-2x%5E2%2B5x-3%29%2F%28%28x-1%29%28x%2B1%29%29=0
%2810x-10%29%2F%28%28x-1%29%28x%2B1%29%29=0
%2810%28x-1%29%29%2F%28%28x-1%29%28x%2B1%29%29=0
10%2F%28x%2B1%29=0
There is no solution.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(2x+3)/(x-1) = 10/(X^2-1)+(2x-3)/(x+1)
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Multiply thru by x^2-1 which equals (x-1)(x+1)
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(2x+3)(x+1) = 10 + (2x-3)(x-1)
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2x^2+5x+3 = 10 + 2x^2-5x +3
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10x = 10
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x = 1
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But x cannot = 1 as that would give you a zero in the denominator.
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Final answer: No solution
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Cheers,
Stan H.