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Question 215979This question is from textbook Intermediate Algebra
: Simplify. [ (x^2 – y^2) / xy ] / (x – y) / y ]
(Entered earlier but put in wrong)
This question is from textbook Intermediate Algebra
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Simplify. 
We have fractions within fractions here and these are difficult to work with. So we will start by rewriting the expression in the form of simple fractions. Remember that fractions represent a division and that divisions can be rewritten as a multiplication by the reciprocal. So we will rewrite the "big" fraction as its numerator times the reciprocal of its denominator:
Now we have a "normal" expression. As you may remember, when multiplying fractions, it is easier to "cross cancel" common factors, if any, before you actually multiply. So we will factor each numerator and denominator and see if we have common factors we can cancel. The first numerator fits the differnce of squares pattern,  , so we can use that pattern to factor it. (I will also factor out a couple of 1's for convenience later.):
Now we can cross cancel the common factors:
leaving
Now we can multiply a much simpler pair of fractions giving:
NOTE: The x's do not cancel in this fraction. The x in the numerator is not a factor of the numerator and only factors can be canceled!). We could, if we want, split this fraction into two (i.e. "unadd"):
This would allow us to cancel the x's in the first fraction giving:
So the answer, depending on which form you prefer, is either or .
P.S. Please use normal minus signs when you enter problems. Algebra.com's formula rendering software cannot handle whatever it is you are typing.
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