SOLUTION: 2x/(x^2 -16)-2/(x-4)=4/(x+4)

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Question 558801: 2x/(x^2 -16)-2/(x-4)=4/(x+4)
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2F%28x%5E2-16%29-2%2F%28x-4%29=4%2F%28x%2B4%29
2x%2F%28x%5E2-16%29=4%2F%28x%2B4%29%2B2%2F%28x-4%29
Take LCD on L.H.S
2x%2F%28x%5E2-16%29=%284%28x-4%29%2B2%28x%2B4%29%29%2F%28x%2B4%29%28x-4%29
2x%2F%28x%5E2-16%29=%284%28x-4%29%2B2%28x%2B4%29%29%2F%28x%5E2-4x%2B4x-16%29
2x%2F%28x%5E2-16%29=%284x-16%2B2x%2B8%29%2F%28x%5E2-cross%284x%29%2Bcross%284x%29-16%29
2x%2F%28x%5E2-16%29=%286x-8%29%2F%28x%5E2-16%29
2x%2Fcross%28x%5E2-16%29=%286x-8%29%2Fcross%28x%5E2-16%29
2x=6x-8
2x-6x=-8
-4x=-8
Divide by -4 both sides of above equation
-4x%2F-4=-8%2F-4
cross%28-4x%29%2Fcross%28-4%29=cross%28-8%29%2Fcross%28-4%29
x=2

Check
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2x%2F%28x%5E2-16%29-2%2F%28x-4%29=4%2F%28x%2B4%29
Put x=2
2%282%29%2F%28%282%29%5E2-16%29-2%2F%282-4%29=4%2F%282%2B4%29
4%2F%284-16%29-2%2F-2=4%2F6
%284%2F-12%29-%282%2F-2%29=4%2F6

%28-1%2F3%29%2B1=2%2F3
%28-1%2B3%29%2F3=2%2F3
2%2F3=2%2F3