Solve 6^-1+6a^-1-2a^-2/frac{a-3{18a^2-72a}}

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

$$\frac{3a^{2}+96a-432-36+144a^{-1}}{a-3}$$

Subtract 36 from -432 to get -468.

$$\frac{3a^{2}+96a-468+144a^{-1}}{a-3}$$

Expand

$$\frac{3\left(a^{3}+32a^{2}-156a+48\right)}{a\left(a-3\right)}$$

Short Solution Steps

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

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

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

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

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

$$\frac{3a^{2}+96a-432-36+144a^{-1}}{a-3}$$

Subtract 36 from -432 to get -468.

$$\frac{3a^{2}+96a-468+144a^{-1}}{a-3}$$