SOLUTION: I am trying to solve this problem but my answer is not the answer in the book. Can you help me figure it out? Here is the equation: x/(x-3) + 4/(x+5)=8x/((x-3)(x+5)) I have a

Algebra ->  Radicals -> SOLUTION: I am trying to solve this problem but my answer is not the answer in the book. Can you help me figure it out? Here is the equation: x/(x-3) + 4/(x+5)=8x/((x-3)(x+5)) I have a      Log On


   

Question 988368: I am trying to solve this problem but my answer is not the answer in the book. Can you help me figure it out? Here is the equation:
x/(x-3) + 4/(x+5)=8x/((x-3)(x+5))
I have a solution set of{-4,3} but the answer key shows the answer as {4}
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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x%2F%28x-3%29+%2B+4%2F%28x%2B5%29=8x%2F%28%28x-3%29%28x%2B5%29%29 Multiply each side by (x-3).
x%2B%284%28x-3%29%29%2F%28x%2B5%29=%288x%29%2F%28x%2B5%29 Multiply each side by (x+5).
%28x%29%28x%2B5%29%2B%284%29%28x-3%29=8x
x%5E2%2B5x%2B4x-12=8x Subtract 8x from each side.
x%5E2%2Bx-12=0
%28x%2B4%29%28x-3%29=0
x%2B4=0 OR x-3=0
x=-4 OR x=3
From the domain of the original equation, we know xdoes not equal 3 or -5
(that would cause division by zero),so we are left with:
ANSWER: x=-4
You can check by putting the value in the original equation:
Negative 4 works, positive four does not,
so there is an error in your book.
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CHECK:
For x=4:
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x%2F%28x-3%29+%2B+4%2F%28x%2B5%29=8x%2F%28%28x-3%29%28x%2B5%29%29
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4%2F%284-3%29%2B4%2F%284%2B5%29=%288%284%29%29%2F%28%284-3%29%284%2B5%29%29
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4%2F1%2B4%2F9=32%2F9
36%2F9%2B4%2F9=32%2F9
40%2F9=32%2F9 False, so 4 is NOT a solution.
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For x=-4:
x%2F%28x-3%29+%2B+4%2F%28x%2B5%29=8x%2F%28%28x-3%29%28x%2B5%29%29
-4%2F%28-4-3%29%2B4%2F%28-4%2B5%29=%288%28-4%29%29%2F%28%28-4-3%29%28-4%2B5%29%29
%28-4%2F-7%29%2B4=%28-32%2F-7%29
4%2F7%29%2B%2828%2F7%29=32%2F7
32%2F7=32%2F7 True, -4 IS our solution.