SOLUTION: How would I solve the following problem? X^-2-Y^-2 _________ X^-1+Y^-1 I understand the first step is to change each varible into a fraction because of the negative expon

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: How would I solve the following problem? X^-2-Y^-2 _________ X^-1+Y^-1 I understand the first step is to change each varible into a fraction because of the negative expon      Log On


   

Question 601808: How would I solve the following problem?
X^-2-Y^-2
_________
X^-1+Y^-1

I understand the first step is to change each varible into a fraction because of the negative exponent.

Answer by w_parminder(53) About Me  (Show Source):
You can put this solution on YOUR website!
I think the question is to simplify
%28X%5E%28-2%29-Y%5E%28-2%29%29%2F%28X%5E%28-1%29%2BY%5E%28-1%29%29
Now using your first step. we get
%28%281%2F%28X%5E2%29%29-%281%2F%28Y%5E2%29%29%29%2F%28%281%2FX%29%2B%281%2FY%29%29
Taking the LCM of Numerator & Denominator separately, we get
%28%28Y%5E2-X%5E2%29%2F%28X%5E2%2AY%5E2%29%29%2F%28%28Y%2BX%29%2F%28X%2AY%29%29
i.e.
%28%28Y%5E2-X%5E2%29%2AX%2AY%29%2F%28X%5E2%2AY%5E2%2A%28Y%2BX%29%29
i.e.
%28%28Y-X%29%28Y%2BX%29%2AX%2AY%29%2F%28X%5E2%2AY%5E2%2A%28Y%2BX%29%29 [Using identity %28a%5E2-b%5E2%29=%28a%2Bb%29%28a-b%29]
i.e.%28Y-X%29%2F%28X%2AY%29
This is the required solution, but It can further be written as
Y%2F%28X%2AY%29-X%2F%28X%2AY%29
i.e.
1%2FX-1%2FY
OR
X%5E%28-1%29-Y%5E%28-1%29