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Mutilplying Through

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Junior | Next Rank: 30 Posts
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by RHINO » Tue Mar 16, 2010 2:45 pm
One of my MGMAT books shows

1/2z - 1/x ==> x-2z/2xz.

I believe this is a very basic step where you "multiply through" with "xz", or something, but I just don't see it for some reason. Can anyone out there break down how exactly this step is done?

Thanks!
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by dmateer25 » Tue Mar 16, 2010 3:30 pm
To subtract fractions, the denominators need to be the same.

so the original problem is:

1/2z - 1/x

The common denominator for these two fractions is 2xz

So to give the first fraction a denominator of 2xz, you need to multiply the numerator and denominator by x. This will leave us with x/2xz.

To give the second fraction a denominator of 2xz, you need to multiply the numerator and denominator by 2z. This will leave us with 2z/2xz

Now we have:

x/2xz - 2z/2xz

Now because the two fraction have a common denominator, we can combine the numerator. Once you combine the numerator, you are left with:

x-2z/2xz
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