Divide (3v^3+v^2+2v)/(9v^3)

$\frac{3 v^{3} + v^{2} + 2 v}{9 v^{3}}$

Step 1

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

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

$\frac{v (3 v^{2}) + v^{2} + 2 v}{9 v^{3}}$

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

$\frac{v (3 v^{2}) + v \cdot v + 2 v}{9 v^{3}}$

Factor $v$ out of $2 v$ .

$\frac{v (3 v^{2}) + v \cdot v + v \cdot 2}{9 v^{3}}$

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

$\frac{v (3 v^{2} + v) + v \cdot 2}{9 v^{3}}$

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

$\frac{v (3 v^{2} + v + 2)}{9 v^{3}}$

Step 2

Cancel the common factors.

Factor $v$ out of $9 v^{3}$ .

$\frac{v (3 v^{2} + v + 2)}{v (9 v^{2})}$

Cancel the common factor.

$\frac{v (3 v^{2} + v + 2)}{v (9 v^{2})}$

Rewrite the expression.

$\frac{3 v^{2} + v + 2}{9 v^{2}}$

Step 3

Split the fraction $\frac{3 v^{2} + v + 2}{9 v^{2}}$ into two fractions.

$\frac{3 v^{2} + v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Step 4

Split the fraction $\frac{3 v^{2} + v}{9 v^{2}}$ into two fractions.

$\frac{3 v^{2}}{9 v^{2}} + \frac{v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Step 5

Cancel the common factor of $3$ and $9$ .

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

$\frac{3 (v^{2})}{9 v^{2}} + \frac{v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Cancel the common factors.

Factor $3$ out of $9 v^{2}$ .

$\frac{3 (v^{2})}{3 (3 v^{2})} + \frac{v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Cancel the common factor.

$\frac{3 v^{2}}{3 (3 v^{2})} + \frac{v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Rewrite the expression.

$\frac{v^{2}}{3 v^{2}} + \frac{v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Step 6

Cancel the common factor of $v^{2}$ .

Cancel the common factor.

$\frac{v^{2}}{3 v^{2}} + \frac{v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Rewrite the expression.

$\frac{1}{3} + \frac{v}{9 v^{2}} + \frac{2}{9 v^{2}}$

Step 7

Cancel the common factor of $v$ and $v^{2}$ .

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

$\frac{1}{3} + \frac{v^{1}}{9 v^{2}} + \frac{2}{9 v^{2}}$

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

$\frac{1}{3} + \frac{v \cdot 1}{9 v^{2}} + \frac{2}{9 v^{2}}$

Cancel the common factors.

Factor $v$ out of $9 v^{2}$ .

$\frac{1}{3} + \frac{v \cdot 1}{v (9 v)} + \frac{2}{9 v^{2}}$

Cancel the common factor.

$\frac{1}{3} + \frac{v \cdot 1}{v (9 v)} + \frac{2}{9 v^{2}}$

Rewrite the expression.

$\frac{1}{3} + \frac{1}{9 v} + \frac{2}{9 v^{2}}$

Divide (3v^3+v^2+2v)/(9v^3)

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