SOLUTION: Help would be great!! x-4/x-5 - 3/x+5 = 10/(x-5)(x+5)

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Question 105706: Help would be great!! x-4/x-5 - 3/x+5 = 10/(x-5)(x+5)

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
:
%28%28x-4%29%29%2F%28%28x-5%29%29 - 3%2F%28%28x%2B5%29%29 = 10%2F%28%28x-5%29%28x%2B5%29%29
:
We can get rid of the denominators if we multiply thru by (x-5)(x+5)
(x-5)(x+5)*%28%28x-4%29%29%2F%28%28x-5%29%29 - (x-5)(x+5)*3%2F%28%28x%2B5%29%29 = (x-5)(x+5)*10%2F%28%28x-5%29%28x%2B5%29%29
:
Cancel out the denominator and you have:
(x+5)(x-4) - 3(x-5) = 10
:
FOIL, then combine like terms on the left:
(x^2 + x - 20) - 3x + 15 = 10
:
x^2 + x - 3x - 20 + 15 - 10 = 0
:
x^2 - 2x - 15 = 0: a quadratic equation, we can factor
:
(x-5)(x+3) = 0
:
x = +5
and
x = -3
:
It's important to notice that x = +5 is NOT a solution, as it produces
division by 0 in the original equation
:
The leaves us with a solution: x = -3
:
Substituting -3 for x in the original equation:
%28%28-3-4%29%29%2F%28%28-3-5%29%29 - 3%2F%28%28-3%2B5%29%29 = 10%2F%28%28-3-5%29%283%2B5%29%29
:
%28%28-7%29%29%2F%28%28-8%29%29 - 3%2F%28%282%29%29 = 10%2F%28%28-8%29%282%29%29
:
%28%287%29%29%2F%28%288%29%29 - 3%2F%28%282%29%29 = 10%2F%28%28-16%29%29
:
%28%2814%29%29%2F%28%2816%29%29 - 24%2F%28%2816%29%29 = -10%2F%28%2816%29%29; confirms our solution
:
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