SOLUTION: x/(x-6)-6/(x+6)=72/(x^2-36)

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Question 442607: x/(x-6)-6/(x+6)=72/(x^2-36)
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x-6%29-6%2F%28x%2B6%29=72%2F%28x%5E2-36%29
Notice x%5E2-36+=++%28x%2B6%29%28x-6%29
Then x%2F%28x-6%29+-+6%2F%28x%2B6%29+=+72%2F%28%28x%2B6%29%28x-6%29%29
What will our common denominator be between these three denominators? (x+6)(x-6), right.
So we can rewrite x%2F%28x-6%29+=+x%28x%2B6%29%2F%28x-6%29%28x%2B6%29
Similarly we can rewrite 6%2F%28x%2B6%29+=+6%28x-6%29%2F%28x%2B6%29%28x-6%29
So now we have %28x%2A%28x%2B6%29+-+6%28x-6%29%29%2F%28x%2B6%29%28x-6%29+=+72%2F%28x%2B6%29%28x-6%29
Now we can solve solely for the numerator.
x%5E2+%2B+6x+-+6x+%2B36+=+x%5E2+%2B+36+=+72
x%5E2+=+36
So x+=+6 and x=-6
But wait! We need to check if these solutions are extraneous. A solution is extraneous if it makes the expression undefined. (AKA: division by 0)
Our denominator is (x+6)(x-6), so it is 0 when x =6 or x=-6.
So both x=6 and x=-6 are EXTRANEOUS!
Thus there is no solution.