Solve m/7-7/m/frac{1{7}+1/m}

$$\frac { \frac { m } { 7 } - \frac { 7 } { m } } { \frac { 1 } { 7 } + \frac { 1 } { m } }$$

Evaluate

$$m-7$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and m is 7m. Multiply \frac{m}{7} times \frac{m}{m}. Multiply \frac{7}{m} times \frac{7}{7}.

$$\frac{\frac{mm}{7m}-\frac{7\times 7}{7m}}{\frac{1}{7}+\frac{1}{m}}$$

Since \frac{mm}{7m} and \frac{7\times 7}{7m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{mm-7\times 7}{7m}}{\frac{1}{7}+\frac{1}{m}}$$

Do the multiplications in mm-7\times 7.

$$\frac{\frac{m^{2}-49}{7m}}{\frac{1}{7}+\frac{1}{m}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and m is 7m. Multiply \frac{1}{7} times \frac{m}{m}. Multiply \frac{1}{m} times \frac{7}{7}.

$$\frac{\frac{m^{2}-49}{7m}}{\frac{m}{7m}+\frac{7}{7m}}$$

Since \frac{m}{7m} and \frac{7}{7m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{m^{2}-49}{7m}}{\frac{m+7}{7m}}$$

Divide \frac{m^{2}-49}{7m} by \frac{m+7}{7m} by multiplying \frac{m^{2}-49}{7m} by the reciprocal of \frac{m+7}{7m}.

$$\frac{\left(m^{2}-49\right)\times 7m}{7m\left(m+7\right)}$$

Cancel out 7m in both numerator and denominator.

$$\frac{m^{2}-49}{m+7}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-7\right)\left(m+7\right)}{m+7}$$

Cancel out m+7 in both numerator and denominator.

$$m-7$$

Expand

$$m-7$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and m is 7m. Multiply \frac{m}{7} times \frac{m}{m}. Multiply \frac{7}{m} times \frac{7}{7}.

$$\frac{\frac{mm}{7m}-\frac{7\times 7}{7m}}{\frac{1}{7}+\frac{1}{m}}$$

Since \frac{mm}{7m} and \frac{7\times 7}{7m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{mm-7\times 7}{7m}}{\frac{1}{7}+\frac{1}{m}}$$

Do the multiplications in mm-7\times 7.

$$\frac{\frac{m^{2}-49}{7m}}{\frac{1}{7}+\frac{1}{m}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and m is 7m. Multiply \frac{1}{7} times \frac{m}{m}. Multiply \frac{1}{m} times \frac{7}{7}.

$$\frac{\frac{m^{2}-49}{7m}}{\frac{m}{7m}+\frac{7}{7m}}$$

Since \frac{m}{7m} and \frac{7}{7m} have the same denominator, add them by adding their numerators.

$$\frac{\frac{m^{2}-49}{7m}}{\frac{m+7}{7m}}$$

Divide \frac{m^{2}-49}{7m} by \frac{m+7}{7m} by multiplying \frac{m^{2}-49}{7m} by the reciprocal of \frac{m+7}{7m}.

$$\frac{\left(m^{2}-49\right)\times 7m}{7m\left(m+7\right)}$$

Cancel out 7m in both numerator and denominator.

$$\frac{m^{2}-49}{m+7}$$

Factor the expressions that are not already factored.

$$\frac{\left(m-7\right)\left(m+7\right)}{m+7}$$

Cancel out m+7 in both numerator and denominator.

$$m-7$$