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x = yz/x + 1/y

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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x = yz/x + 1/y

by alindawit » Fri Jun 03, 2011 7:14 pm
If x = yz/x + 1/y; and xy is not equal to 0, which of the following expressions is equal to z?

The answer given is:

x(xy - 1) / y2

derived by doing the following calculations:

step 1: x - 1/y = yz/x
step 2: x2 - x/y2 = z
step 3: x2y/y2 - x/y2 = z

result: x(xy -1) / y2

I now don't understand what happens at step 3. Why is also the nominator multiplied by y?
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by smackmartine » Fri Jun 03, 2011 7:21 pm
x = yz/x + 1/y

step 1: x - 1/y = yz/x

step 2: x^2/y - x/y^2 = z (you did not divide the 1st variable,x^2 by y)

step 3: [x^2 (y) - x]/y^2 =z (taking y^2 as LCM)

step 4: x(xy-1)/y^2 = z
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by alindawit » Fri Jun 03, 2011 9:25 pm
you are totally right, I forgot, thanks!
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