Simplify the complex fraction.
-$$\frac { m ^ { - 1 } + z ^ { - 1 } } { m ^ { - 1 } - z ^ { - 1 } }$$
A) $\frac { z + m } { z - m }$
B) $\frac { \mathrm { z } + \mathrm { m } } { \mathrm { m } }$
C) $\frac { \mathrm { z } + \mathrm { m } } { \mathrm { z } }$
D) $\frac { \mathrm { z } - \mathrm { m } } { \mathrm { z } }$

Question

Quizplus · Accepted Answer

To simplify the given complex fraction, we convert the negative exponents to positive by taking the reciprocal. Thus, $m^{-1} = \frac{1}{m}$ and $z^{-1} = \frac{1}{z}$. Substituting these into the fraction gives us $\frac{\frac{1}{m} + \frac{1}{z}}{\frac{1}{m} - \frac{1}{z}}$. Finding a common denominator for both the numerator and the denominator, we get $\frac{\frac{z + m}{zm}}{\frac{z - m}{zm}}$, which simplifies to $\frac{z + m}{z - m}$, matching choice A.

Simplify the Complex Fraction m−1+z−1m−1−z−1\frac { m ^ { - 1 } + z ^ { - 1 } } { m ^ { - 1 } - z ^ { - 1 } }m−1−z−1m−1+z−1​

Simplify the Complex Fraction $\frac { m ^ { - 1 } + z ^ { - 1 } } { m ^ { - 1 } - z ^ { - 1 } }$