Solve 8m/m-2-6/5m+5

$$\frac { 8 m } { m - 2 } - \frac { 6 } { 5 m + 5 }$$

Evaluate

$$\frac{2\left(20m^{2}+17m+6\right)}{5\left(m-2\right)\left(m+1\right)}$$

Short Solution Steps

Factor 5m+5.

$$\frac{8m}{m-2}-\frac{6}{5\left(m+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m-2 and 5\left(m+1\right) is 5\left(m-2\right)\left(m+1\right). Multiply \frac{8m}{m-2} times \frac{5\left(m+1\right)}{5\left(m+1\right)}. Multiply \frac{6}{5\left(m+1\right)} times \frac{m-2}{m-2}.

$$\frac{8m\times 5\left(m+1\right)}{5\left(m-2\right)\left(m+1\right)}-\frac{6\left(m-2\right)}{5\left(m-2\right)\left(m+1\right)}$$

Since \frac{8m\times 5\left(m+1\right)}{5\left(m-2\right)\left(m+1\right)} and \frac{6\left(m-2\right)}{5\left(m-2\right)\left(m+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8m\times 5\left(m+1\right)-6\left(m-2\right)}{5\left(m-2\right)\left(m+1\right)}$$

Do the multiplications in 8m\times 5\left(m+1\right)-6\left(m-2\right).

$$\frac{40m^{2}+40m-6m+12}{5\left(m-2\right)\left(m+1\right)}$$

Combine like terms in 40m^{2}+40m-6m+12.

$$\frac{40m^{2}+34m+12}{5\left(m-2\right)\left(m+1\right)}$$

Expand 5\left(m-2\right)\left(m+1\right).

$$\frac{40m^{2}+34m+12}{5m^{2}-5m-10}$$

Factor

$$\frac{2\left(20m^{2}+17m+6\right)}{5\left(m-2\right)\left(m+1\right)}$$