Solve k^2+7k+10/k^2+8k+15*k^2+3k/k^2-7k-18

$$\frac { k ^ { 2 } + 7 k + 10 } { k ^ { 2 } + 8 k + 15 } \cdot \frac { k ^ { 2 } + 3 k } { k ^ { 2 } - 7 k - 18 }$$

Evaluate

$$\frac{k}{k-9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+7k+10}{k^{2}+8k+15}.

$$\frac{\left(k+2\right)\left(k+5\right)}{\left(k+3\right)\left(k+5\right)}\times \frac{k^{2}+3k}{k^{2}-7k-18}$$

Cancel out k+5 in both numerator and denominator.

$$\frac{k+2}{k+3}\times \frac{k^{2}+3k}{k^{2}-7k-18}$$

Multiply \frac{k+2}{k+3} times \frac{k^{2}+3k}{k^{2}-7k-18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(k+2\right)\left(k^{2}+3k\right)}{\left(k+3\right)\left(k^{2}-7k-18\right)}$$

Factor the expressions that are not already factored.

$$\frac{k\left(k+2\right)\left(k+3\right)}{\left(k-9\right)\left(k+2\right)\left(k+3\right)}$$

Cancel out \left(k+2\right)\left(k+3\right) in both numerator and denominator.

$$\frac{k}{k-9}$$

Expand

$$\frac{k}{k-9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+7k+10}{k^{2}+8k+15}.

$$\frac{\left(k+2\right)\left(k+5\right)}{\left(k+3\right)\left(k+5\right)}\times \frac{k^{2}+3k}{k^{2}-7k-18}$$

Cancel out k+5 in both numerator and denominator.

$$\frac{k+2}{k+3}\times \frac{k^{2}+3k}{k^{2}-7k-18}$$

Multiply \frac{k+2}{k+3} times \frac{k^{2}+3k}{k^{2}-7k-18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(k+2\right)\left(k^{2}+3k\right)}{\left(k+3\right)\left(k^{2}-7k-18\right)}$$

Factor the expressions that are not already factored.

$$\frac{k\left(k+2\right)\left(k+3\right)}{\left(k-9\right)\left(k+2\right)\left(k+3\right)}$$

Cancel out \left(k+2\right)\left(k+3\right) in both numerator and denominator.

$$\frac{k}{k-9}$$