SOLUTION: solve the following equation for x 3/x-3+7/x+3=5x/x^2-9 these are 3 fractions, I get close, but somehow get messed up

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Question 463386: solve the following equation for x
3/x-3+7/x+3=5x/x^2-9
these are 3 fractions, I get close, but somehow get messed up
Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
3/(x - 3) + 7/(x + 3) = 5x/(x² - 9)
3/(x - 3) + 7/(x + 3) = 5x/(x + 3)(x - 3) {factored x² - 9 into (x + 3)(x - 3)}

Multiply entire equation by least common denominator (x + 3)(x - 3)
(x + 3)(x - 3)[3/(x - 3) + 7/(x + 3) = 5x/(x + 3)(x - 3)]

Multiply each term by (x + 3)(x - 3)
(x + 3)(x - 3)[3/(x - 3)] + (x + 3)(x - 3)[7/(x + 3)] = (x + 3)(x - 3)5x/(x + 3)(x - 3)]

3(x + 3) + 7(x - 3) = 5x {cancelled and multiplied what's left}
3x + 9 + 7x - 21 = 5x {used distributive property}
10x - 12 = 5x {combined like terms}
-12 = -5x {subtracted 10x from both sides}
x = 12/5 {divided both sides by -5}

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