Solve k^2+12k+32/k^2+16k+64*k^2+8k/k^2+8k+16

$$\frac { k ^ { 2 } + 12 k + 32 } { k ^ { 2 } + 16 k + 64 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 8 k + 16 }$$

Evaluate

$$\frac{k}{k+4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+12k+32}{k^{2}+16k+64}.

$$\frac{\left(k+4\right)\left(k+8\right)}{\left(k+8\right)^{2}}\times \frac{k^{2}+8k}{k^{2}+8k+16}$$

Cancel out k+8 in both numerator and denominator.

$$\frac{k+4}{k+8}\times \frac{k^{2}+8k}{k^{2}+8k+16}$$

Multiply \frac{k+4}{k+8} times \frac{k^{2}+8k}{k^{2}+8k+16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(k+4\right)\left(k^{2}+8k\right)}{\left(k+8\right)\left(k^{2}+8k+16\right)}$$

Factor the expressions that are not already factored.

$$\frac{k\left(k+4\right)\left(k+8\right)}{\left(k+8\right)\left(k+4\right)^{2}}$$

Cancel out \left(k+4\right)\left(k+8\right) in both numerator and denominator.

$$\frac{k}{k+4}$$

Expand

$$\frac{k}{k+4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+12k+32}{k^{2}+16k+64}.

$$\frac{\left(k+4\right)\left(k+8\right)}{\left(k+8\right)^{2}}\times \frac{k^{2}+8k}{k^{2}+8k+16}$$

Cancel out k+8 in both numerator and denominator.

$$\frac{k+4}{k+8}\times \frac{k^{2}+8k}{k^{2}+8k+16}$$

Multiply \frac{k+4}{k+8} times \frac{k^{2}+8k}{k^{2}+8k+16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(k+4\right)\left(k^{2}+8k\right)}{\left(k+8\right)\left(k^{2}+8k+16\right)}$$

Factor the expressions that are not already factored.

$$\frac{k\left(k+4\right)\left(k+8\right)}{\left(k+8\right)\left(k+4\right)^{2}}$$

Cancel out \left(k+4\right)\left(k+8\right) in both numerator and denominator.

$$\frac{k}{k+4}$$