Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { x ^ { 2 } - 25 y ^ { - 2 } } { \left( x - 5 y ^ { - 1 } \right) \left( x + 5 y ^ { - 1 } \right) }$$
A) $- 1$
B) $\frac { y ^ { 2 } - x } { x y - 5 }$
C) 1
D) $\frac { x y ^ { 2 } } { y - x }$

Question

Quizplus · Accepted Answer

The expression simplifies to 1 because the numerator is a difference of squares, $x^2 - (5y^{-1})^2$, and the denominator is the factored form of the numerator, $(x - 5y^{-1})(x + 5y^{-1})$. When divided, they cancel out, leaving 1.

Perform the Indicated Operation and Write Your Answer with Positive x2−25y−2(x−5y−1)(x+5y−1)\frac { x ^ { 2 } - 25 y ^ { - 2 } } { \left( x - 5 y ^ { - 1 } \right) \left( x + 5 y ^ { - 1 } \right) }(x−5y−1)(x+5y−1)x2−25y−2​

Perform the Indicated Operation and Write Your Answer with Positive $\frac { x ^ { 2 } - 25 y ^ { - 2 } } { \left( x - 5 y ^ { - 1 } \right) \left( x + 5 y ^ { - 1 } \right) }$