Solve (a+1)^4-1/2a(a+1)^2

$$\frac { ( a + 1 ) ^ { 4 } - 1 } { 2 a ( a + 1 ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out a in both numerator and denominator.

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

Expand the expression.

$$\frac{a^{3}+4a^{2}+6a+4}{2a^{2}+4a+2}$$

Expand

$$\frac{a^{3}+4a^{2}+6a+4}{2\left(a+1\right)^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out a in both numerator and denominator.

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

Expand the expression.

$$\frac{a^{3}+4a^{2}+6a+4}{2a^{2}+4a+2}$$