Solve m^2-30/m-6+6/6-m

$$\frac { m ^ { 2 } - 30 } { m - 6 } + \frac { 6 } { 6 - m }$$

Evaluate

$$m+6$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m-6 and 6-m is m-6. Multiply \frac{6}{6-m} times \frac{-1}{-1}.

$$\frac{m^{2}-30}{m-6}+\frac{6\left(-1\right)}{m-6}$$

Since \frac{m^{2}-30}{m-6} and \frac{6\left(-1\right)}{m-6} have the same denominator, add them by adding their numerators.

$$\frac{m^{2}-30+6\left(-1\right)}{m-6}$$

Do the multiplications in m^{2}-30+6\left(-1\right).

$$\frac{m^{2}-30-6}{m-6}$$

Combine like terms in m^{2}-30-6.

$$\frac{m^{2}-36}{m-6}$$

Factor the expressions that are not already factored in \frac{m^{2}-36}{m-6}.

$$\frac{\left(m-6\right)\left(m+6\right)}{m-6}$$

Cancel out m-6 in both numerator and denominator.

$$m+6$$

Expand

$$m+6$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m-6 and 6-m is m-6. Multiply \frac{6}{6-m} times \frac{-1}{-1}.

$$\frac{m^{2}-30}{m-6}+\frac{6\left(-1\right)}{m-6}$$

Since \frac{m^{2}-30}{m-6} and \frac{6\left(-1\right)}{m-6} have the same denominator, add them by adding their numerators.

$$\frac{m^{2}-30+6\left(-1\right)}{m-6}$$

Do the multiplications in m^{2}-30+6\left(-1\right).

$$\frac{m^{2}-30-6}{m-6}$$

Combine like terms in m^{2}-30-6.

$$\frac{m^{2}-36}{m-6}$$

Factor the expressions that are not already factored in \frac{m^{2}-36}{m-6}.

$$\frac{\left(m-6\right)\left(m+6\right)}{m-6}$$

Cancel out m-6 in both numerator and denominator.

$$m+6$$