Solve 91/m^2-169+7/2(m+13)

$$\frac { 91 } { m ^ { 2 } - 169 } + \frac { 7 } { 2 ( m + 13 ) }$$

Evaluate

$$\frac{7}{2\left(m-13\right)}$$

Short Solution Steps

Factor m^{2}-169.

$$\frac{91}{\left(m-13\right)\left(m+13\right)}+\frac{7}{2\left(m+13\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-13\right)\left(m+13\right) and 2\left(m+13\right) is 2\left(m-13\right)\left(m+13\right). Multiply \frac{91}{\left(m-13\right)\left(m+13\right)} times \frac{2}{2}. Multiply \frac{7}{2\left(m+13\right)} times \frac{m-13}{m-13}.

$$\frac{91\times 2}{2\left(m-13\right)\left(m+13\right)}+\frac{7\left(m-13\right)}{2\left(m-13\right)\left(m+13\right)}$$

Since \frac{91\times 2}{2\left(m-13\right)\left(m+13\right)} and \frac{7\left(m-13\right)}{2\left(m-13\right)\left(m+13\right)} have the same denominator, add them by adding their numerators.

$$\frac{91\times 2+7\left(m-13\right)}{2\left(m-13\right)\left(m+13\right)}$$

Do the multiplications in 91\times 2+7\left(m-13\right).

$$\frac{182+7m-91}{2\left(m-13\right)\left(m+13\right)}$$

Combine like terms in 182+7m-91.

$$\frac{91+7m}{2\left(m-13\right)\left(m+13\right)}$$

Factor the expressions that are not already factored in \frac{91+7m}{2\left(m-13\right)\left(m+13\right)}.

$$\frac{7\left(m+13\right)}{2\left(m-13\right)\left(m+13\right)}$$

Cancel out m+13 in both numerator and denominator.

$$\frac{7}{2\left(m-13\right)}$$

Expand 2\left(m-13\right).

$$\frac{7}{2m-26}$$

Expand

$$\frac{7}{2\left(m-13\right)}$$

Short Solution Steps

Factor m^{2}-169.

$$\frac{91}{\left(m-13\right)\left(m+13\right)}+\frac{7}{2\left(m+13\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-13\right)\left(m+13\right) and 2\left(m+13\right) is 2\left(m-13\right)\left(m+13\right). Multiply \frac{91}{\left(m-13\right)\left(m+13\right)} times \frac{2}{2}. Multiply \frac{7}{2\left(m+13\right)} times \frac{m-13}{m-13}.

$$\frac{91\times 2}{2\left(m-13\right)\left(m+13\right)}+\frac{7\left(m-13\right)}{2\left(m-13\right)\left(m+13\right)}$$

Since \frac{91\times 2}{2\left(m-13\right)\left(m+13\right)} and \frac{7\left(m-13\right)}{2\left(m-13\right)\left(m+13\right)} have the same denominator, add them by adding their numerators.

$$\frac{91\times 2+7\left(m-13\right)}{2\left(m-13\right)\left(m+13\right)}$$

Do the multiplications in 91\times 2+7\left(m-13\right).

$$\frac{182+7m-91}{2\left(m-13\right)\left(m+13\right)}$$

Combine like terms in 182+7m-91.

$$\frac{91+7m}{2\left(m-13\right)\left(m+13\right)}$$

Factor the expressions that are not already factored in \frac{91+7m}{2\left(m-13\right)\left(m+13\right)}.

$$\frac{7\left(m+13\right)}{2\left(m-13\right)\left(m+13\right)}$$

Cancel out m+13 in both numerator and denominator.

$$\frac{7}{2\left(m-13\right)}$$

Expand 2\left(m-13\right).

$$\frac{7}{2m-26}$$