SOLUTION: Help would be great!! x-4/x-5

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

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) (Show Source): You can put this solution on YOUR website!
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- =
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We can get rid of the denominators if we multiply thru by (x-5)(x+5)
(x-5)(x+5)* - (x-5)(x+5)* = (x-5)(x+5)*
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Cancel out the denominator and you have:
(x+5)(x-4) - 3(x-5) = 10
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FOIL, then combine like terms on the left:
(x^2 + x - 20) - 3x + 15 = 10
:
x^2 + x - 3x - 20 + 15 - 10 = 0
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x^2 - 2x - 15 = 0: a quadratic equation, we can factor
:
(x-5)(x+3) = 0
:
x = +5
and
x = -3
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It's important to notice that x = +5 is NOT a solution, as it produces
division by 0 in the original equation
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The leaves us with a solution: x = -3
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Substituting -3 for x in the original equation:
- =
:
- =
:
- =
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- = -; confirms our solution
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