SOLUTION: I need help adding the following fraction. y / (x2 - xy) - x / (y2 – xy)

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Question 308597: I need help adding the following fraction.
y / (x2 - xy) - x / (y2 – xy)
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
y+%2F+%28x2+-+xy%29++-++x+%2F+%28y2+-+xy%29

First, factor the denominators so you can find the LCD.
y+%2F%28x%28x+-y%29%29++-++x+%2F+%28y%28y+-+x%29%29

The next step is a nice "trick" to help find the LCD. Multiply the numerator and denominator of the second fraction by -1, which makes the second denominator look more like the first one!
y+%2F%28x%28x+-y%29%29++%2B++x+%2F+%28y%28x+-+y%29%29

Now, the LCD+=+xy%28x-y%29.

Multiply the numerator and denominator of the first fraction by y, and the second fraction by x:

%28y%5E2%29%2F%28xy%28x-y%29%29+%2B+%28x%5E2%29%2F%28xy%28x-y%29%29+
%28y%5E2%2Bx%5E2%29%2F%28xy%28x-y%29%29

The numerator does NOT factor, so the fraction does NOT reduce!!

You may want to see my website for help with FRACTIONS! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. For written explanations, look for "Basic, Intermediate, and College Algebra: One Step at a Time", choose "Basic Algebra" and look for "Chapter 3 Fractions." See also the "MATH IN LIVING COLOR" pages that go with this explanation, where the exercises are solved IN COLOR!

For VIDEO explanations, on my Homepage look for "Rapalje Videos in Living Color". Choose "Intermediate Algebra" and select the topics of "Fractions." While this is Intermediate Algebra, portions of it are suitable for a first level algebra class. This and other videos are from my own classroom a few years ago before I retired. They are all FREE!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus