Solve [-5/6a^4-2/3a(+5/2a-5/4a^3)+(frac{1}{2}a-1)(frac{1}{2}a+1)]:(+frac{1}{12}a^2)

$$[ - \frac { 5 } { 6 } a ^ { 4 } - \frac { 2 } { 3 } a ( + \frac { 5 } { 2 } a - \frac { 5 } { 4 } a ^ { 3 } ) + ( \frac { 1 } { 2 } a - 1 ) ( \frac { 1 } { 2 } a + 1 ) ] : ( + \frac { 1 } { 12 } a ^ { 2 } )$$

Evaluate

$$-17-\frac{12}{a^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{12}\left(-17a^{2}-12\right)}{\frac{1}{12}a^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{-17a^{2}-12}{\left(\frac{1}{12}\right)^{0}a^{2}}$$

Expand the expression.

$$\frac{-17a^{2}-12}{a^{2}}$$

Expand

$$-17-\frac{12}{a^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{12}\left(-17a^{2}-12\right)}{\frac{1}{12}a^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{-17a^{2}-12}{\left(\frac{1}{12}\right)^{0}a^{2}}$$

Expand the expression.

$$\frac{-17a^{2}-12}{a^{2}}$$