Algebra Examples

$(18 x^{3} + 12 x^{2} - 3 x) \div 6 x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{18 x^{3} + 12 x^{2} - 3 x}{6 x^{2}}$

Step 2

Factor $3 x$ out of $18 x^{3} + 12 x^{2} - 3 x$ .

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Step 2.1

Factor $3 x$ out of $18 x^{3}$ .

$\frac{3 x (6 x^{2}) + 12 x^{2} - 3 x}{6 x^{2}}$

Step 2.2

Factor $3 x$ out of $12 x^{2}$ .

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

Step 2.3

Factor $3 x$ out of $- 3 x$ .

$\frac{3 x (6 x^{2}) + 3 x (4 x) + 3 x (- 1)}{6 x^{2}}$

Step 2.4

Factor $3 x$ out of $3 x (6 x^{2}) + 3 x (4 x)$ .

$\frac{3 x (6 x^{2} + 4 x) + 3 x (- 1)}{6 x^{2}}$

Step 2.5

Factor $3 x$ out of $3 x (6 x^{2} + 4 x) + 3 x (- 1)$ .

$\frac{3 x (6 x^{2} + 4 x - 1)}{6 x^{2}}$

Step 3

Cancel the common factor of $3$ and $6$ .

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Step 3.1

Factor $3$ out of $3 x (6 x^{2} + 4 x - 1)$ .

$\frac{3 (x (6 x^{2} + 4 x - 1))}{6 x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{3 (x (6 x^{2} + 4 x - 1))}{3 (2 x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (x (6 x^{2} + 4 x - 1))}{3 (2 x^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{x (6 x^{2} + 4 x - 1)}{2 x^{2}}$

Step 4

Cancel the common factors.

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Step 4.1

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

$\frac{x (6 x^{2} + 4 x - 1)}{x (2 x)}$

Step 4.2

Cancel the common factor.

$\frac{x (6 x^{2} + 4 x - 1)}{x (2 x)}$

Step 4.3

Rewrite the expression.

$\frac{6 x^{2} + 4 x - 1}{2 x}$

Step 5

Split the fraction $\frac{6 x^{2} + 4 x - 1}{2 x}$ into two fractions.

$\frac{6 x^{2} + 4 x}{2 x} + \frac{- 1}{2 x}$

Step 6

Split the fraction $\frac{6 x^{2} + 4 x}{2 x}$ into two fractions.

$\frac{6 x^{2}}{2 x} + \frac{4 x}{2 x} + \frac{- 1}{2 x}$

Step 7

Cancel the common factor of $6$ and $2$ .

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Step 7.1

Factor $2$ out of $6 x^{2}$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2 x$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

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

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Step 8.1

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

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

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

Step 8.2.2

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

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

Step 8.2.3

Cancel the common factor.

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

Step 8.2.4

Rewrite the expression.

$\frac{3 x}{1} + \frac{4 x}{2 x} + \frac{- 1}{2 x}$

Step 8.2.5

Divide $3 x$ by $1$ .

$3 x + \frac{4 x}{2 x} + \frac{- 1}{2 x}$

Step 9

Cancel the common factor of $4$ and $2$ .

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Step 9.1

Factor $2$ out of $4 x$ .

$3 x + \frac{2 (2 x)}{2 x} + \frac{- 1}{2 x}$

Step 9.2

Cancel the common factor.

$3 x + \frac{2 (2 x)}{2 x} + \frac{- 1}{2 x}$

Step 9.3

Rewrite the expression.

$3 x + 2 + \frac{- 1}{2 x}$

Step 10

Move the negative in front of the fraction.

$3 x + 2 - \frac{1}{2 x}$