Simplify.
-$$\frac { \frac { 1 } { m } + \frac { 1 } { \mathrm { z } } } { \frac { 1 } { \mathrm {~m} } - \frac { 1 } { \mathrm { z } } }$$

Question

Quizplus · Accepted Answer

To simplify, we first need to find a common denominator in both the numerator and denominator of the fraction. The common denominator is mz, so:

$$\frac { \frac { 1 } { m } + \frac { 1 } { \mathrm { z } } } { \frac { 1 } { \mathrm {~m} } - \frac { 1 } { \mathrm { z } } } = \frac{\frac{z+m}{mz}}{\frac{z-m}{mz}}$$

We can then simplify by multiplying the numerator by the reciprocal of the denominator:

$$\frac{\frac{z+m}{mz}}{\frac{z-m}{mz}} = \frac{z+m}{mz}\cdot \frac{mz}{z-m} = \frac{z+m}{z-m}\cdot \frac{1}{m} = \boxed{\textbf{(D)}\ \frac{z+m}{z-m}}\cdot \frac { 1 } { m }$$

Simplify - 1m+1z1 m−1z\frac { \frac { 1 } { m } + \frac { 1 } { \mathrm { z } } } { \frac { 1 } { \mathrm {~m} } - \frac { 1 } { \mathrm { z } } } m1​−z1​m1​+z1​​

Simplify
- $\frac { \frac { 1 } { m } + \frac { 1 } { \mathrm { z } } } { \frac { 1 } { \mathrm {~m} } - \frac { 1 } { \mathrm { z } } }$