Solve 1/frac{frac{1{M}+1/N}{alpha}}

$$\frac { 1 } { \frac { \frac { 1 } { M } + \frac { 1 } { N } } { \alpha } }$$

Evaluate

$$\frac{MN\alpha }{M+N}$$

Solution Steps

Divide 1 by \frac{\frac{1}{M}+\frac{1}{N}}{\alpha } by multiplying 1 by the reciprocal of \frac{\frac{1}{M}+\frac{1}{N}}{\alpha }.

$$\frac{\alpha }{\frac{1}{M}+\frac{1}{N}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of M and N is MN. Multiply \frac{1}{M} times \frac{N}{N}. Multiply \frac{1}{N} times \frac{M}{M}.

$$\frac{\alpha }{\frac{N}{MN}+\frac{M}{MN}}$$

Since \frac{N}{MN} and \frac{M}{MN} have the same denominator, add them by adding their numerators.

$$\frac{\alpha }{\frac{N+M}{MN}}$$

Divide \alpha by \frac{N+M}{MN} by multiplying \alpha by the reciprocal of \frac{N+M}{MN}.

$$\frac{\alpha MN}{N+M}$$

Expand

$$\frac{MN\alpha }{M+N}$$

Solution Steps

Divide 1 by \frac{\frac{1}{M}+\frac{1}{N}}{\alpha } by multiplying 1 by the reciprocal of \frac{\frac{1}{M}+\frac{1}{N}}{\alpha }.

$$\frac{\alpha }{\frac{1}{M}+\frac{1}{N}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of M and N is MN. Multiply \frac{1}{M} times \frac{N}{N}. Multiply \frac{1}{N} times \frac{M}{M}.

$$\frac{\alpha }{\frac{N}{MN}+\frac{M}{MN}}$$

Since \frac{N}{MN} and \frac{M}{MN} have the same denominator, add them by adding their numerators.

$$\frac{\alpha }{\frac{N+M}{MN}}$$

Divide \alpha by \frac{N+M}{MN} by multiplying \alpha by the reciprocal of \frac{N+M}{MN}.

$$\frac{\alpha MN}{N+M}$$