Solve w^2-16/4w+16div2w^2-16w+32/8w+32

$$\frac { w ^ { 2 } - 16 } { 4 w + 16 } \div \frac { 2 w ^ { 2 } - 16 w + 32 } { 8 w + 32 }$$

Evaluate

$$\frac{w+4}{w-4}$$

Short Solution Steps

Divide \frac{w^{2}-16}{4w+16} by \frac{2w^{2}-16w+32}{8w+32} by multiplying \frac{w^{2}-16}{4w+16} by the reciprocal of \frac{2w^{2}-16w+32}{8w+32}.

$$\frac{\left(w^{2}-16\right)\left(8w+32\right)}{\left(4w+16\right)\left(2w^{2}-16w+32\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(w-4\right)\left(w+4\right)^{2}}{2\times 4\left(w+4\right)\left(w-4\right)^{2}}$$

Cancel out 2\times 4\left(w-4\right)\left(w+4\right) in both numerator and denominator.

$$\frac{w+4}{w-4}$$

Expand

$$\frac{w+4}{w-4}$$

Short Solution Steps

Divide \frac{w^{2}-16}{4w+16} by \frac{2w^{2}-16w+32}{8w+32} by multiplying \frac{w^{2}-16}{4w+16} by the reciprocal of \frac{2w^{2}-16w+32}{8w+32}.

$$\frac{\left(w^{2}-16\right)\left(8w+32\right)}{\left(4w+16\right)\left(2w^{2}-16w+32\right)}$$

Factor the expressions that are not already factored.

$$\frac{8\left(w-4\right)\left(w+4\right)^{2}}{2\times 4\left(w+4\right)\left(w-4\right)^{2}}$$

Cancel out 2\times 4\left(w-4\right)\left(w+4\right) in both numerator and denominator.

$$\frac{w+4}{w-4}$$