Solve n/7-7/n/frac{1{7}+1/n}=

$$\frac { \frac { n } { 7 } - \frac { 7 } { n } } { \frac { 1 } { 7 } + \frac { 1 } { n } } =$$

Evaluate

$$n-7$$

Short Solution Steps

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

$$\frac{\frac{nn}{7n}-\frac{7\times 7}{7n}}{\frac{1}{7}+\frac{1}{n}}$$

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

$$\frac{\frac{nn-7\times 7}{7n}}{\frac{1}{7}+\frac{1}{n}}$$

Do the multiplications in nn-7\times 7.

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

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

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

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

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

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

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

Cancel out 7n in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out n+7 in both numerator and denominator.

$$n-7$$

Expand

$$n-7$$

Short Solution Steps

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

$$\frac{\frac{nn}{7n}-\frac{7\times 7}{7n}}{\frac{1}{7}+\frac{1}{n}}$$

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

$$\frac{\frac{nn-7\times 7}{7n}}{\frac{1}{7}+\frac{1}{n}}$$

Do the multiplications in nn-7\times 7.

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

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

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

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

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

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

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

Cancel out 7n in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out n+7 in both numerator and denominator.

$$n-7$$