SOLUTION: x/x-2 - x-5/5 = x-2/5

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Question 196960: x/x-2 - x-5/5 = x-2/5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x-2%29-%28x-5%29%2F5=%28x-2%29%2F5 Start with the given equation.


Multiply EVERY term by the LCD 5%28x-2%29 to clear out the fractions.


5x-%28x-2%29%28x-5%29=%28x-2%29%28x-2%29 Simplify


5x-%28x%5E2-7x%2B10%29=x%5E2-4x%2B4 FOIL


5x-x%5E2%2B7x-10=x%5E2-4x%2B4 Distribute


5x-x%5E2%2B7x-10-x%5E2%2B4x-4=0 Get all terms to the left side.


-2x%5E2%2B16x-14=0 Combine like terms.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=-2, B=16, and C=-14


Let's use the quadratic formula to solve for x


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%2816%29+%2B-+sqrt%28+%2816%29%5E2-4%28-2%29%28-14%29+%29%29%2F%282%28-2%29%29 Plug in A=-2, B=16, and C=-14


x+=+%28-16+%2B-+sqrt%28+256-4%28-2%29%28-14%29+%29%29%2F%282%28-2%29%29 Square 16 to get 256.


x+=+%28-16+%2B-+sqrt%28+256-112+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%28-14%29 to get 112


x+=+%28-16+%2B-+sqrt%28+144+%29%29%2F%282%28-2%29%29 Subtract 112 from 256 to get 144


x+=+%28-16+%2B-+sqrt%28+144+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x+=+%28-16+%2B-+12%29%2F%28-4%29 Take the square root of 144 to get 12.


x+=+%28-16+%2B+12%29%2F%28-4%29 or x+=+%28-16+-+12%29%2F%28-4%29 Break up the expression.


x+=+%28-4%29%2F%28-4%29 or x+=++%28-28%29%2F%28-4%29 Combine like terms.


x+=+1 or x+=+7 Simplify.


So the solutions are x+=+1 or x+=+7