Simplify (12m^4-24m^3+6m^2+9m-9)/(6m^2)

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

Step 1

Factor $3$ out of $12 m^{4}$ .

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

Step 2

Factor $3$ out of $- 24 m^{3}$ .

$\frac{3 (4 m^{4}) + 3 (- 8 m^{3}) + 6 m^{2} + 9 m - 9}{6 m^{2}}$

Step 3

Factor $3$ out of $3 (4 m^{4}) + 3 (- 8 m^{3})$ .

$\frac{3 (4 m^{4} - 8 m^{3}) + 6 m^{2} + 9 m - 9}{6 m^{2}}$

Step 4

Factor $3$ out of $6 m^{2}$ .

$\frac{3 (4 m^{4} - 8 m^{3}) + 3 (2 m^{2}) + 9 m - 9}{6 m^{2}}$

Step 5

Factor $3$ out of $3 (4 m^{4} - 8 m^{3}) + 3 (2 m^{2})$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2}) + 9 m - 9}{6 m^{2}}$

Step 6

Factor $3$ out of $9 m$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2}) + 3 (3 m) - 9}{6 m^{2}}$

Step 7

Factor $3$ out of $3 (4 m^{4} - 8 m^{3} + 2 m^{2}) + 3 (3 m)$ .

$\frac{3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m) - 9}{6 m^{2}}$

Step 8

Factor $3$ out of $- 9$ .

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

Step 9

Factor $3$ out of $3 (4 m^{4} - 8 m^{3} + 2 m^{2} + 3 m) + 3 (- 3)$ .

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

Step 10

Cancel the common factors.

Factor $3$ out of $6 m^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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