Solve frac{2a^{4}-2a^{2}+3a^2+3a^4}{(a^2+a)(a-a^2)(a+1)(a-1)}=

$$\frac { 2 a ^ { 4 } - 2 a ^ { 2 } + 3 a ^ { 2 } + 3 a ^ { 4 } } { ( a ^ { 2 } + a ) ( a - a ^ { 2 } ) ( a + 1 ) ( a - 1 ) } =$$

Evaluate

$$-\frac{5a^{2}+1}{\left(1-a^{2}\right)^{2}}$$

Short Solution Steps

Combine -2a^{2} and 3a^{2} to get a^{2}.

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

Combine 2a^{4} and 3a^{4} to get 5a^{4}.

$$\frac{5a^{4}+a^{2}}{\left(a^{2}+a\right)\left(a-a^{2}\right)\left(a+1\right)\left(a-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{a^{2}\left(5a^{2}+1\right)}{\left(a-1\right)\left(-a+1\right)a^{2}\left(a+1\right)^{2}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{5a^{2}+1}{\left(a-1\right)\left(-a+1\right)\left(a+1\right)^{2}}$$

Expand the expression.

$$\frac{5a^{2}+1}{-a^{4}+2a^{2}-1}$$

Expand

$$-\frac{5a^{2}+1}{\left(1-a^{2}\right)^{2}}$$

Short Solution Steps

Combine -2a^{2} and 3a^{2} to get a^{2}.

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

Combine 2a^{4} and 3a^{4} to get 5a^{4}.

$$\frac{5a^{4}+a^{2}}{\left(a^{2}+a\right)\left(a-a^{2}\right)\left(a+1\right)\left(a-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{a^{2}\left(5a^{2}+1\right)}{\left(a-1\right)\left(-a+1\right)a^{2}\left(a+1\right)^{2}}$$

Cancel out a^{2} in both numerator and denominator.

$$\frac{5a^{2}+1}{\left(a-1\right)\left(-a+1\right)\left(a+1\right)^{2}}$$

Expand the expression.

$$\frac{5a^{2}+1}{-a^{4}+2a^{2}-1}$$