SOLUTION: 4-x/x-2=-2/x-2

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Question 321308: 4-x/x-2=-2/x-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%284-x%29%2F%28x-2%29=-2%2F%28x-2%29 Start with the given equation.


%284-x%29%28x-2%29=-2%28x-2%29 Cross multiply.


4x-8-x%5E2%2B2x=-2%28x-2%29 FOIL


4x-8-x%5E2%2B2x=-2x%2B4 Distribute.


4x-8-x%5E2%2B2x%2B2x-4=0 Get every term to the left side.


-x%5E2%2B8x-12=0 Combine like terms.


Notice that the quadratic -x%5E2%2B8x-12 is in the form of Ax%5E2%2BBx%2BC where A=-1, B=8, and C=-12


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-%288%29+%2B-+sqrt%28+%288%29%5E2-4%28-1%29%28-12%29+%29%29%2F%282%28-1%29%29 Plug in A=-1, B=8, and C=-12


x+=+%28-8+%2B-+sqrt%28+64-4%28-1%29%28-12%29+%29%29%2F%282%28-1%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64-48+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-12%29 to get 48


x+=+%28-8+%2B-+sqrt%28+16+%29%29%2F%282%28-1%29%29 Subtract 48 from 64 to get 16


x+=+%28-8+%2B-+sqrt%28+16+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%28-8+%2B-+4%29%2F%28-2%29 Take the square root of 16 to get 4.


x+=+%28-8+%2B+4%29%2F%28-2%29 or x+=+%28-8+-+4%29%2F%28-2%29 Break up the expression.


x+=+%28-4%29%2F%28-2%29 or x+=++%28-12%29%2F%28-2%29 Combine like terms.


x+=+2 or x+=+6 Simplify.


So the possible solutions are x+=+2 or x+=+6


However, if you plug in x+=+2 into the original equation, you'll get a division by zero error. So x%3C%3E2


This means that the only solution is x+=+6