# How do you write the rational expression (x^3+5x^2+6x)/x^-4 in simplest form?

The answer is: ${x}^{7} + 5 {x}^{6} + 6 {x}^{5}$, simply remembering that:
$\frac{1}{x} ^ - 4 = {x}^{4}$, and so:
$\frac{{x}^{3} + 5 {x}^{2} + 6 x}{x} ^ - 4 = \left({x}^{3} + 5 {x}^{2} + 6 x\right) {x}^{4} = {x}^{7} + 5 {x}^{6} + 6 {x}^{5} = {x}^{5} \left({x}^{2} + 5 x + 6\right) = {x}^{5} \left(x + 2\right) \left(x + 3\right)$.
This is because I found the two numers whose sum is $5$ and whose product is $6$ ($a = 1$, $b = 5$ and $c = 6$, if $a \ne 1$ another way to factor has to be used).