Solve (-2/3a^6+1/3a^4+4/5a^2):(-2/9a^3)

$$( - \frac { 2 } { 3 } a ^ { 6 } + \frac { 1 } { 3 } a ^ { 4 } + \frac { 4 } { 5 } a ^ { 2 } ) : ( - \frac { 2 } { 9 } a ^ { 3 } )$$

Evaluate

$$3a^{3}-\frac{3a}{2}-\frac{18}{5a}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{-\frac{1}{15}\times 10a^{2}\left(a^{2}-\left(-\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)\left(a^{2}-\left(\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)}{-\frac{2}{9}a^{3}}$$

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

$$\frac{-\frac{1}{15}\times 10\left(a^{2}-\left(-\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)\left(a^{2}-\left(\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)}{-\frac{2}{9}a}$$

Expand the expression.

$$\frac{-\frac{2}{3}a^{4}+\frac{1}{3}a^{2}+\frac{4}{5}}{-\frac{2}{9}a}$$

Expand

$$3a^{3}-\frac{3a}{2}-\frac{18}{5a}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{-\frac{1}{15}\times 10a^{2}\left(a^{2}-\left(-\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)\left(a^{2}-\left(\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)}{-\frac{2}{9}a^{3}}$$

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

$$\frac{-\frac{1}{15}\times 10\left(a^{2}-\left(-\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)\left(a^{2}-\left(\frac{1}{20}\sqrt{505}+\frac{1}{4}\right)\right)}{-\frac{2}{9}a}$$

Expand the expression.

$$\frac{-\frac{2}{3}a^{4}+\frac{1}{3}a^{2}+\frac{4}{5}}{-\frac{2}{9}a}$$