SOLUTION: Can you help me simplify this expression, using only positive exponents in the answer...I don't quite understand these, so if you could be detailed, I would appriciate it. {{{

Algebra ->  Functions -> SOLUTION: Can you help me simplify this expression, using only positive exponents in the answer...I don't quite understand these, so if you could be detailed, I would appriciate it. {{{      Log On


   

Question 122901: Can you help me simplify this expression, using only positive exponents in the answer...I don't quite understand these, so if you could be detailed, I would appriciate it.

%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29 Start with given expression


%281%2Fx-1%2Fy%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 Flip the bases that have negative exponents. Remember x%5E-1=1%2Fx%5E1=1%2Fx and x%5E-2=1%2Fx%5E2



%28%28y%2Fy%29%281%2Fx%29-%28x%2Fx%29%281%2Fy%29%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 Multiply the first fraction 1%2Fx by y%2Fy. Multiply the second fraction 1%2Fy by x%2Fx.


%28y%2Fxy-x%2Fxy%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 Multiply the fractions


%28%28y-x%29%2F%28xy%29%29%2F%281%2Fx%5E2-1%2Fy%5E2%29 Combine the fractions in the numerator

Multiply the first fraction 1%2Fx%5E2 by y%5E2%2Fy%5E2. Multiply the second fraction 1%2Fy%5E2 by x%5E2%2Fx%5E2.


Multiply the fractions



%28%28y-x%29%2F%28xy%29%29%2F%28%28y%5E2-x%5E2%29%2F%28x%5E2y%5E2%29%29 Combine the fractions in the denominator


%28%28y-x%29%2F%28xy%29%29%2A%28%28x%5E2y%5E2%29%2F%28y%5E2-x%5E2%29%29 Multiply the first fraction by the reciprocal of the second fraction



%28%28y-x%29%2F%28xy%29%29%2A%28%28x%2Ax%2Ay%2Ay%29%2F%28%28y-x%29%28y%2Bx%29%29%29 Factor x%5E2y%5E2 to get x%2Ax%2Ay%2Ay. Factor y%5E2-x%5E2 (by using the difference of squares formula) to get %28y-x%29%28y%2Bx%29.



Cancel like terms



xy%2F%28y%2Bx%29 Simplify



Answer:

So %28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29 simplifies to xy%2F%28y%2Bx%29

In other words, %28x%5E-1-y%5E-1%29%2F%28x%5E-2-y%5E-2%29=xy%2F%28y%2Bx%29