SOLUTION: Solve (5-x)/(2-x)-(3-2x)/(2x)=1

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Question 195667: Solve (5-x)/(2-x)-(3-2x)/(2x)=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285-x%29%2F%282-x%29-%283-2x%29%2F%282x%29=1 Start with the given equation.


Multiply every term on both sides by the LCD 2x%282-x%29. Doing this will eliminate all of the fractions.


2x%285-x%29-%282-x%29%283-2x%29=2x%282-x%29%281%29 Cancel out and simplify


2x%285-x%29-%282-x%29%283-2x%29=2x%282-x%29 Multiply


2x%285-x%29-%286-7x%2B2x%5E2%29=2x%282-x%29 FOIL


10x-2x%5E2-6%2B7x-2x%5E2=4x-2x%5E2 Distribute


10x-2x%5E2-6%2B7x-2x%5E2-4x%2B2x%5E2=0 Get all terms to the left side.


-2x%5E2%2B13x-6=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=-2, b=13, and c=-6


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-%2813%29+%2B-+sqrt%28+%2813%29%5E2-4%28-2%29%28-6%29+%29%29%2F%282%28-2%29%29 Plug in a=-2, b=13, and c=-6


x+=+%28-13+%2B-+sqrt%28+169-4%28-2%29%28-6%29+%29%29%2F%282%28-2%29%29 Square 13 to get 169.


x+=+%28-13+%2B-+sqrt%28+169-48+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%28-6%29 to get 48


x+=+%28-13+%2B-+sqrt%28+121+%29%29%2F%282%28-2%29%29 Subtract 48 from 169 to get 121


x+=+%28-13+%2B-+sqrt%28+121+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x+=+%28-13+%2B-+11%29%2F%28-4%29 Take the square root of 121 to get 11.


x+=+%28-13+%2B+11%29%2F%28-4%29 or x+=+%28-13+-+11%29%2F%28-4%29 Break up the expression.


x+=+%28-2%29%2F%28-4%29 or x+=++%28-24%29%2F%28-4%29 Combine like terms.


x+=+1%2F2 or x+=+6 Simplify.


So the answers are x+=+1%2F2 or x+=+6