Solve (6^-1+(6a)-2a^2):(a-3/18a^2-72a)

$$( 6 ^ { - 1 } + ( 6 a ) - 2 a ^ { 2 } ) : ( \frac { a - 3 } { 18 a ^ { 2 } - 72 a } )$$

Evaluate

$$\frac{3a\left(a-4\right)\left(1+36a-12a^{2}\right)}{a-3}$$

Short Solution Steps

Divide 6^{-1}+6a-2a^{2} by \frac{a-3}{18a^{2}-72a} by multiplying 6^{-1}+6a-2a^{2} by the reciprocal of \frac{a-3}{18a^{2}-72a}.

$$\frac{\left(6^{-1}+6a-2a^{2}\right)\left(18a^{2}-72a\right)}{a-3}$$

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\frac{\left(\frac{1}{6}+6a-2a^{2}\right)\left(18a^{2}-72a\right)}{a-3}$$

Use the distributive property to multiply \frac{1}{6}+6a-2a^{2} by 18a^{2}-72a and combine like terms.

$$\frac{-429a^{2}-12a+252a^{3}-36a^{4}}{a-3}$$

Expand

$$-\frac{3\left(12a^{4}-84a^{3}+143a^{2}+4a\right)}{a-3}$$

Short Solution Steps

Divide 6^{-1}+6a-2a^{2} by \frac{a-3}{18a^{2}-72a} by multiplying 6^{-1}+6a-2a^{2} by the reciprocal of \frac{a-3}{18a^{2}-72a}.

$$\frac{\left(6^{-1}+6a-2a^{2}\right)\left(18a^{2}-72a\right)}{a-3}$$

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\frac{\left(\frac{1}{6}+6a-2a^{2}\right)\left(18a^{2}-72a\right)}{a-3}$$

Use the distributive property to multiply \frac{1}{6}+6a-2a^{2} by 18a^{2}-72a and combine like terms.

$$\frac{-429a^{2}-12a+252a^{3}-36a^{4}}{a-3}$$