Perform the indicated operation and write your answer with positive integer exponents.
-$\frac { m ^ { - 1 } - n ^ { - 1 } } { ( m n ) ^ { - 1 } }$
A) $n - m$
B) $m - n$
C) $- \mathrm { n } - \mathrm { m }$
D) $m + n$ m

Question

Quizplus · Accepted Answer

To simplify the given expression, we first find a common denominator for the numerator and then simplify the entire fraction. The expression is $\frac { m ^ { - 1 } - n ^ { - 1 } } { ( m n ) ^ { - 1 } }$. The numerator can be written as $\frac{n - m}{mn}$ by finding a common denominator (mn) for $m^{-1}$ and $n^{-1}$. The entire expression then becomes $\frac{\frac{n - m}{mn}}{(mn)^{-1}}$, which simplifies to $n - m$ because dividing by $(mn)^{-1}$ is the same as multiplying by $mn$, and the $mn$ terms cancel out.

Perform the Indicated Operation and Write Your Answer with Positive m−1−n−1(mn)−1\frac { m ^ { - 1 } - n ^ { - 1 } } { ( m n ) ^ { - 1 } }(mn)−1m−1−n−1​

Perform the Indicated Operation and Write Your Answer with Positive $\frac { m ^ { - 1 } - n ^ { - 1 } } { ( m n ) ^ { - 1 } }$