SOLUTION: Simplify. {{{ 5/(x^2 - xy) - 5/(y^2 - xy) }}}

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Question 440167: Simplify. +5%2F%28x%5E2+-+xy%29+-+5%2F%28y%5E2+-+xy%29+
Found 2 solutions by rwm, rapaljer:
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
factor
x^2-xy=x*(x-y)
y^2-xy=y*(y-x)
y-x=-(x-y)
so we can write it.
+5%2F%28%28x%29%2A%28x-y%29%29-5%2F%28-y%2A%28x-y%29%29
+5%2F%28%28x%29%2A%28x-y%29%29%2B5%2F%28y%2A%28x-y%29%29
+5y%2F%28%28xy%29%2A%28x-y%29%29%2B5x%2F%28xy%2A%28x-y%29%29
+%285x%2B5y%29%2F%28%28xy%29%2A%28x-y%29%29
+5%2A%28x%2By%29%2F%28%28xy%29%2A%28x-y%29%29

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%28x%28x-y%29%29-5%2F%28y%28y-x%29%29+

5%2F%28x%28x-y%29%29%2B5%2F%28y%28x-y%29%29+

The LCD is xy(x-y), so multiply the numerator and denominator of the first fraction by y and the second fraction by x.

%285y%29%2F%28xy%28x-y%29%29+%2B+%285x%29%2F%28xy%28x-y%29%29+
%285y%2B5x%29%2F%28xy%28x-y%29%29
%285%28y%2Bx%29%29%2F%28xy%28x-y%29%29+

For additional explanation, examples, exercises, and ALL the answers, please see my own website. Click on my tutor name "rapaljer" anywhere in algebra.com. The link you find there will take you to the Homepage of my website. From the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in Chapter 3 for the topics on Adding and Subtracting Fractions. My explanations were written especially for students who have trouble with math, with many of my excercises solved in detail on the MATH IN LIVING COLOR pages that go with these sections.

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