Solve -2/3a^6+1/3a^4+4/15a^3/-frac{2{9}a^3}

$$\frac{ - \frac{ 2 }{ 3 } { a }^{ 6 } + \frac{ 1 }{ 3 } { a }^{ 4 } + \frac{ 4 }{ 15 } { a }^{ 3 } }{ - \frac{ 2 }{ 9 } { a }^{ 3 } }$$

Evaluate

$$3a^{3}-\frac{3a}{2}-\frac{6}{5}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{15}a^{3}\left(-10a^{3}+5a+4\right)}{-\frac{2}{9}a^{3}}$$

Cancel out a^{3} in both numerator and denominator.

$$\frac{\frac{1}{15}\left(-10a^{3}+5a+4\right)}{-\frac{2}{9}}$$

Expand the expression.

$$\frac{-\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15}}{-\frac{2}{9}}$$

Divide -\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15} by -\frac{2}{9} by multiplying -\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15} by the reciprocal of -\frac{2}{9}.

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

Use the distributive property to multiply -\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15} by 9.

$$\frac{-6a^{3}+3a+\frac{12}{5}}{-2}$$

Expand

$$3a^{3}-\frac{3a}{2}-\frac{6}{5}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{15}a^{3}\left(-10a^{3}+5a+4\right)}{-\frac{2}{9}a^{3}}$$

Cancel out a^{3} in both numerator and denominator.

$$\frac{\frac{1}{15}\left(-10a^{3}+5a+4\right)}{-\frac{2}{9}}$$

Expand the expression.

$$\frac{-\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15}}{-\frac{2}{9}}$$

Divide -\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15} by -\frac{2}{9} by multiplying -\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15} by the reciprocal of -\frac{2}{9}.

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

Use the distributive property to multiply -\frac{2}{3}a^{3}+\frac{1}{3}a+\frac{4}{15} by 9.

$$\frac{-6a^{3}+3a+\frac{12}{5}}{-2}$$