Simplify:

\[
\frac{x^{-2} - y^{-2}}{x^{-1} - y^{-1}}
\]

so negative exponents mean reciprocals so x^-1=1/(x^1)
x^-2=1/(x^2) x^-2=1/(y^2) so ([1/(x^2)]-[1/(y^2]) is the diffarence of two perfect squares which is (x^-2-y^-2)=(1/x-1/y)(1/x+1/y)
so that equals (1/x-1/y)(1/x+1/y)
(x^-1)=1/x y^-1=1/y the bottom is (1/x-1/y) so the equation is [(1/x-1/y)(1/x+1/y)]/(1/x-1/y) we can cancell out the (1/x-1/y) on the top and the bottom and be left with (1/x-1/y)/1 or 1/x-1/y

Answered by apologiabiology | 2024-06-10

By rewriting the expression using the definitions of negative exponents, we simplify the expression x − 1 − y − 1 x − 2 − y − 2 ​ to x 1 ​ + y 1 ​ . This uses the difference of squares formula for the numerator and cancels out the common denominator. Therefore, the final result is x 1 ​ + y 1 ​ .
;

Answered by apologiabiology | 2025-06-12