SOLUTION: I need help, please! Simplify {{{(x^-2-y^-2)/(x^-1-y^-1)}}}

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: I need help, please! Simplify {{{(x^-2-y^-2)/(x^-1-y^-1)}}}      Log On


   

Question 18865: I need help, please!
Simplify
%28x%5E-2-y%5E-2%29%2F%28x%5E-1-y%5E-1%29
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E-2-y%5E-2%29%2F%28x%5E-1-y%5E-1%29
A negative power means that you can put the reciprocal of that number
ie. x^-2 is the same as (1/x^2)


keeping that in mind,this expression becomes
%28%281%2Fx%5E2%29-%281%2Fy%5E2%29%29%2F%28%281%2Fx%29-%281%2Fy%29%29
Taking LCM this becomes,
%28%28y%5E2-x%5E2%29%2F%28x%5E2%2Ay%5E2%29%29%2F%28%28y-x%29%2F%28xy%29%29
Now we get,
%28%28y%5E2-x%5E2%29%2F%28x%5E2%2Ay%5E2%29%29%2A%28%28xy%29%2F%28y-x%29%29
**(y^2-x^2)=(y-x)(y+x).Substituting this we get,
+%28%28y-x%29%28y%2Bx%29%2F%28x%5E2%2Ay%5E2%29%29%2A%28%28xy%29%2F%28y-x%29%29+
**(x^2*y^2)=(xy)(xy).Substituting this we get,
+%28%28y-x%29%28y%2Bx%29%2F%28xy%2Axy%29%29%2A%28%28xy%29%2F%28y-x%29%29+
Now cancelling out terms we get,
+%28%28y%2Bx%29%2F%28xy%29%29+
And this is the final answer.


Hope this helps,
Prabhat