Solve k^2+5k+6/k^2-2k-15*2k^2-10k/k^2+2k

$$\frac { k ^ { 2 } + 5 k + 6 } { k ^ { 2 } - 2 k - 15 } \times \frac { 2 k ^ { 2 } - 10 k } { k ^ { 2 } + 2 k }$$

Evaluate

$$2$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+5k+6}{k^{2}-2k-15}.

$$\frac{\left(k+2\right)\left(k+3\right)}{\left(k-5\right)\left(k+3\right)}\times \frac{2k^{2}-10k}{k^{2}+2k}$$

Cancel out k+3 in both numerator and denominator.

$$\frac{k+2}{k-5}\times \frac{2k^{2}-10k}{k^{2}+2k}$$

Factor the expressions that are not already factored in \frac{2k^{2}-10k}{k^{2}+2k}.

$$\frac{k+2}{k-5}\times \frac{2k\left(k-5\right)}{k\left(k+2\right)}$$

Cancel out k in both numerator and denominator.

$$\frac{k+2}{k-5}\times \frac{2\left(k-5\right)}{k+2}$$

Multiply \frac{k+2}{k-5} times \frac{2\left(k-5\right)}{k+2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(k+2\right)\times 2\left(k-5\right)}{\left(k-5\right)\left(k+2\right)}$$

Cancel out \left(k-5\right)\left(k+2\right) in both numerator and denominator.

$$2$$

Factor

$$2$$