SOLUTION: (x/(x+5))-((5/(x-5))=14 find the value of x

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Question 1171633: (x/(x+5))-((5/(x-5))=14
find the value of x
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


+x%2F%28x%2B5%29+-+5%2F%28x-5%29+=+14+



Multiply both sides by (x+5)(x-5), and you get:

++x%28x-5%29+-+5%28x%2B5%29+=+14%28x%2B5%29%28x-5%29+



Combine & simplify (steps shown):

++%28x%5E2-5x%29+-+%285x%2B25%29+=+14%28x%5E2-25%29+

++x%5E2-10x-25+=+14x%5E2-350+

+13x%5E2%2B10x-325+=+0+



Here I just used the quadratic formula:  for ax%5E2+%2B+bx+%2B+c+=+0+, you get 

 +x+=+%281%2F%282a%29%29%28-b+%2B-+sqrt%28b%5E2-4ac%29%29+





+x+=+%281%2F%282%2A13%29%29%28+-10+%2B-sqrt%28100-4%2813%29%28-325%29%29%29+



+x+=+%281%2F%282%2A13%29%29%28+-10+%2B-sqrt%28100%2A170%29%29%29+

+x+=+%281%2F%282%2A13%29%29%28+-10+%2B-+10%2Asqrt%28170%29%29%29+

+highlight%28+x+=+%285%2F13%29%28+-1+%2B-sqrt%28170%29%29%29%29++   <--- exact answer

 



Approximate answer:

+x=-5.399336+

and

+x=4.630156+



Plug in these values for x and you will see they both result in approx 14.