msu08

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y= x +2/ x-3, then which of the following represents x?

answer is (3y +2)/(y-1)

can anyone help work out this problem? i'm not sure how this is solved. thanks!
 

Vicviper

Michael De Coro, DMD - AKA Steve McAwesome
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Okey doke! Here we go:

y= (x+2) / (x-3)

Multiply both sides by (x-3) to get:

(x-3):thumbup: = x +2

Destribute that out to get:

xy-3y = x+2

Subtract two from each side to get:

xy-3y-2 = x

Now subtract xy from both sides to get:

-3y-2 = x-xy

Now on the right side, factor out X to get:

-3y-2 = x(1-y)

Then just devide both sides by (1-y) to get:

(-3y-2) / (1-y) = X

Now at this point, you'd be done solving the problem, because this answer IS correct, but it's not one of the answer choices. SO, notice that your answer looks very similar, with just some signs changes, so we're going to multiply only the left side by (-1) / (-1). You're only doing this to the left side because -1/-1 still equals 1, and so by identity definition, it doesn't change either side. and we should end up with:

(3y+2) / (-1+y) = X ... note that (-1+y) = (y-1) and there ya go!

Hope that helps!

(3y+2) / (1+y) = X
 
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