Solve a^2-4a+16/a^2-16*(a+4)(a^2-8a+16)/-9a^2+36a-144=?

$$\frac { a ^ { 2 } - 4 a + 16 } { a ^ { 2 } - 16 } \times \frac { ( a + 4 ) ( a ^ { 2 } - 8 a + 16 ) } { - 9 a ^ { 2 } + 36 a - 144 } = ?$$

Evaluate

$$\frac{4-a}{9}$$

Short Solution Steps

Use the distributive property to multiply a+4 by a^{2}-8a+16 and combine like terms.

$$\frac{a^{2}-4a+16}{a^{2}-16}\times \frac{a^{3}-4a^{2}-16a+64}{-9a^{2}+36a-144}$$

Multiply \frac{a^{2}-4a+16}{a^{2}-16} times \frac{a^{3}-4a^{2}-16a+64}{-9a^{2}+36a-144} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-4a+16\right)\left(a^{3}-4a^{2}-16a+64\right)}{\left(a^{2}-16\right)\left(-9a^{2}+36a-144\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a+4\right)\left(a-4\right)^{2}\left(a^{2}-4a+16\right)}{9\left(a-4\right)\left(a+4\right)\left(-a^{2}+4a-16\right)}$$

Extract the negative sign in a^{2}-4a+16.

$$\frac{-\left(a+4\right)\left(a-4\right)^{2}\left(-a^{2}+4a-16\right)}{9\left(a-4\right)\left(a+4\right)\left(-a^{2}+4a-16\right)}$$

Cancel out \left(a-4\right)\left(a+4\right)\left(-a^{2}+4a-16\right) in both numerator and denominator.

$$\frac{-\left(a-4\right)}{9}$$

Expand the expression.

$$\frac{-a+4}{9}$$

Expand

$$\frac{4-a}{9}$$

Short Solution Steps

Use the distributive property to multiply a+4 by a^{2}-8a+16 and combine like terms.

$$\frac{a^{2}-4a+16}{a^{2}-16}\times \frac{a^{3}-4a^{2}-16a+64}{-9a^{2}+36a-144}$$

Multiply \frac{a^{2}-4a+16}{a^{2}-16} times \frac{a^{3}-4a^{2}-16a+64}{-9a^{2}+36a-144} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(a^{2}-4a+16\right)\left(a^{3}-4a^{2}-16a+64\right)}{\left(a^{2}-16\right)\left(-9a^{2}+36a-144\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(a+4\right)\left(a-4\right)^{2}\left(a^{2}-4a+16\right)}{9\left(a-4\right)\left(a+4\right)\left(-a^{2}+4a-16\right)}$$

Extract the negative sign in a^{2}-4a+16.

$$\frac{-\left(a+4\right)\left(a-4\right)^{2}\left(-a^{2}+4a-16\right)}{9\left(a-4\right)\left(a+4\right)\left(-a^{2}+4a-16\right)}$$

Cancel out \left(a-4\right)\left(a+4\right)\left(-a^{2}+4a-16\right) in both numerator and denominator.

$$\frac{-\left(a-4\right)}{9}$$

Expand the expression.

$$\frac{-a+4}{9}$$