SOLUTION: Please help me simplify this equation: {{{ ((1/x^2)-(1/y^2))/((1/x)+(1/y)) }}}

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Question 9827: Please help me simplify this equation: +%28%281%2Fx%5E2%29-%281%2Fy%5E2%29%29%2F%28%281%2Fx%29%2B%281%2Fy%29%29+
Answer by prince_abubu(198) About Me  (Show Source):
You can put this solution on YOUR website!
+%28%281%2Fx%5E2%29-%281%2Fy%5E2%29%29%2F%28%281%2Fx%29%2B%281%2Fy%29%29+ <------------ Start here

+%28%281%2Fx+-+1%2Fy%29%281%2Fx+%2B+1%2Fy%29%29%2F%281%2Fx+%2B+1%2Fy%29+ <------------ The numerator really is a difference of squares. Remember that if you've got something in the form +a%5E2+-+b%5E2+, it's really +%28a+%2B+b%29%28a+-+b%29+. It's one of those special types of quadratic forms.

+1%2Fx+-+1%2Fy+ <-------- The +1%2Fx+%2B+1%2Fy+'s in the numerator and denominator cancel. You're now left with this.

TIP: The whole point of simplifying rational expressions, aka, those with fairly long numerators and denominators, is to write it out in as few terms and symbols as possible. Since it's a fraction, they're EXTREMELY LIKELY to choose expressions in the numerator and denominator so that when rearranged, you'll get common terms in the numerator and denominator that are meant to be cancelled. When you see a rational expression, or rational equation and they ask you to simplify, count on cancelling terms somewhere in the process.