SOLUTION: a/b=x-y/y-z solve for y

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Question 132636: a/b=x-y/y-z
solve for y
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Fb=%28x-y%29%2F%28y-z%29 Start with the given equation


a%28y-z%29=b%28x-y%29 Cross multiply


ay-az=bx-by Distribute


-az=bx-by-ay Subtract ay from both sides


-az-bx=-by-ay Subtract bx from both sides


-az-bx=y%28-b-a%29 Factor out the GCF "y" from the right side

%28-az-bx%29%2F%28-b-a%29=y Divide both sides by -b-a


y=%28-az-bx%29%2F%28-b-a%29 Rearrange the equation


y=%28-1%28az%2Bbx%29%29%2F%28-b-a%29 Factor out -1 from the numerator


y=%28-1%28az%2Bbx%29%29%2F%28-1%28b%2Ba%29%29 Factor out -1 from the denominator


y=cross%28-1%29%28az%2Bbx%29%2Fcross%28-1%29%28b%2Ba%29 Cancel out the "-1" terms


y=%28az%2Bbx%29%2F%28b%2Ba%29 Simplify