# How do you simplify the expression (12m^4-24m^3+6m^2+9m-9)/(6m^2)?

Jun 12, 2017

#### Answer:

$\frac{1}{2} {m}^{2} - \frac{5}{2} m + 1$

#### Explanation:

Let's start with the original problem:

$\frac{12 {m}^{4} - 24 {m}^{3} + 6 {m}^{2} + 9 m - 9}{6 {m}^{2}}$

We can rewrite the expression like so:

$\frac{12 {m}^{4}}{6 {m}^{2}} - \frac{24 {m}^{3}}{6 {m}^{2}} + \frac{6 {m}^{2}}{6 {m}^{2}} + \frac{9 m}{6 {m}^{2}} - \frac{9}{6 {m}^{2}}$

Now we can simplify each of the terms in the expression:

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

We can get rid of the negative exponent:

$2 {m}^{2} - 4 m + 1 + \frac{3}{2 m} - \frac{3}{2 {m}^{2}}$

We then rearrange the expression from the highest power to the lowest power and combine like terms:

$2 {m}^{2} - \frac{3}{2 {m}^{2}} - 4 m + \frac{3}{2 m} + 1$

$\frac{1}{2} {m}^{2} - \frac{5}{2} m + 1$

Hope this helped!

Jun 12, 2017

#### Answer:

(12m^4-24m^3+6m^2+9m-9)/(6m^2)=color(blue)((4m^4-8m^3+2m^2+3m-3)/(2m^2)

#### Explanation:

Simplify:

$\frac{12 {m}^{4} - 24 {m}^{3} + 6 {m}^{2} + 9 m - 9}{6 {m}^{2}}$

Factor out the common factor $3$ in the numerator.

$\frac{3 \left(4 {m}^{4} - 8 {m}^{3} + 2 {m}^{2} + 3 m - 3\right)}{6 {m}^{2}}$

Divide $6$ in the denominator by $3$ in the numerator.

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{3}^{1}}}} \left(4 {m}^{4} - 8 {m}^{3} + 2 {m}^{2} + 3 m - 3\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{{6}^{2}}}} {m}^{2}}$

Simplify.

$\frac{4 {m}^{4} - 8 {m}^{3} + 2 {m}^{2} + 3 m - 3}{2 {m}^{2}}$