Solve frac{w^{4}-1}{w^{3}-1}*frac{w^{2}+w^3+w^4}{2w^2+w^4+1}

$$\frac { w ^ { 4 } - 1 } { w ^ { 3 } - 1 } \cdot \frac { w ^ { 2 } + w ^ { 3 } + w ^ { 4 } } { 2 w ^ { 2 } + w ^ { 4 } + 1 }$$

Evaluate

$$\frac{\left(w+1\right)w^{2}}{w^{2}+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{w^{4}-1}{w^{3}-1}.

$$\frac{\left(w-1\right)\left(w+1\right)\left(w^{2}+1\right)}{\left(w-1\right)\left(w^{2}+w+1\right)}\times \frac{w^{2}+w^{3}+w^{4}}{2w^{2}+w^{4}+1}$$

Cancel out w-1 in both numerator and denominator.

$$\frac{\left(w+1\right)\left(w^{2}+1\right)}{w^{2}+w+1}\times \frac{w^{2}+w^{3}+w^{4}}{2w^{2}+w^{4}+1}$$

Multiply \frac{\left(w+1\right)\left(w^{2}+1\right)}{w^{2}+w+1} times \frac{w^{2}+w^{3}+w^{4}}{2w^{2}+w^{4}+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(w+1\right)\left(w^{2}+1\right)\left(w^{2}+w^{3}+w^{4}\right)}{\left(w^{2}+w+1\right)\left(2w^{2}+w^{4}+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(w+1\right)w^{2}\left(w^{2}+1\right)\left(w^{2}+w+1\right)}{\left(w^{2}+w+1\right)\left(w^{2}+1\right)^{2}}$$

Cancel out \left(w^{2}+1\right)\left(w^{2}+w+1\right) in both numerator and denominator.

$$\frac{\left(w+1\right)w^{2}}{w^{2}+1}$$

Expand the expression.

$$\frac{w^{3}+w^{2}}{w^{2}+1}$$

Expand

$$\frac{w^{3}+w^{2}}{w^{2}+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{w^{4}-1}{w^{3}-1}.

$$\frac{\left(w-1\right)\left(w+1\right)\left(w^{2}+1\right)}{\left(w-1\right)\left(w^{2}+w+1\right)}\times \frac{w^{2}+w^{3}+w^{4}}{2w^{2}+w^{4}+1}$$

Cancel out w-1 in both numerator and denominator.

$$\frac{\left(w+1\right)\left(w^{2}+1\right)}{w^{2}+w+1}\times \frac{w^{2}+w^{3}+w^{4}}{2w^{2}+w^{4}+1}$$

Multiply \frac{\left(w+1\right)\left(w^{2}+1\right)}{w^{2}+w+1} times \frac{w^{2}+w^{3}+w^{4}}{2w^{2}+w^{4}+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(w+1\right)\left(w^{2}+1\right)\left(w^{2}+w^{3}+w^{4}\right)}{\left(w^{2}+w+1\right)\left(2w^{2}+w^{4}+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(w+1\right)w^{2}\left(w^{2}+1\right)\left(w^{2}+w+1\right)}{\left(w^{2}+w+1\right)\left(w^{2}+1\right)^{2}}$$

Cancel out \left(w^{2}+1\right)\left(w^{2}+w+1\right) in both numerator and denominator.

$$\frac{\left(w+1\right)w^{2}}{w^{2}+1}$$

Expand the expression.

$$\frac{w^{3}+w^{2}}{w^{2}+1}$$