Simplify (4v^3-3v^2+v)/v

$\frac{4 v^{3} - 3 v^{2} + v}{v}$

Step 1

Factor $v$ out of $4 v^{3} - 3 v^{2} + v$ .

Factor $v$ out of $4 v^{3}$ .

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

Factor $v$ out of $- 3 v^{2}$ .

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

Raise $v$ to the power of $1$ .

$\frac{v (4 v^{2}) + v (- 3 v) + v^{1}}{v}$

Factor $v$ out of $v^{1}$ .

$\frac{v (4 v^{2}) + v (- 3 v) + v \cdot 1}{v}$

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

$\frac{v (4 v^{2} - 3 v) + v \cdot 1}{v}$

Factor $v$ out of $v (4 v^{2} - 3 v) + v \cdot 1$ .

$\frac{v (4 v^{2} - 3 v + 1)}{v}$

Step 2

Cancel the common factor of $v$ .

Cancel the common factor.

$\frac{v (4 v^{2} - 3 v + 1)}{v}$

Divide $4 v^{2} - 3 v + 1$ by $1$ .

$4 v^{2} - 3 v + 1$