Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Factor $3$ out of $- 6 x$ .

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

Step 1.3

Factor $3$ out of $3$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Move the negative in front of the fraction.

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

Step 3

Factor $- 1$ out of $- 2 x^{2}$ .

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

Step 4

Factor $- 1$ out of $- 2 x$ .

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

Step 5

Factor $- 1$ out of $- (2 x^{2}) - (2 x)$ .

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

Step 6

Rewrite $1$ as $- 1 (- 1)$ .

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

Step 7

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

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

Step 8

Rewrite $- (2 x^{2} + 2 x - 1)$ as $- 1 (2 x^{2} + 2 x - 1)$ .

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

Step 9

Move the negative in front of the fraction.

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

Step 10

Multiply $- 1$ by $- 1$ .

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

Step 11

Multiply $\frac{3 (2 x^{2} + 2 x - 1)}{2 x}$ by $1$ .

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

Step 12

Apply the distributive property.

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

Step 13

Simplify.

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Step 13.1

Multiply $2$ by $3$ .

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

Step 13.2

Multiply $2$ by $3$ .

$\frac{6 x^{2} + 6 x + 3 \cdot - 1}{2 x}$

Step 13.3

Multiply $3$ by $- 1$ .

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

Step 14

Split the fraction $\frac{6 x^{2} + 6 x - 3}{2 x}$ into two fractions.

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

Step 15

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

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

Step 16

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

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Step 16.1

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

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

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor $2$ out of $2 x$ .

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

Step 16.2.2

Cancel the common factor.

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

Step 16.2.3

Rewrite the expression.

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

Step 17

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

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Step 17.1

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

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

Step 17.2

Cancel the common factors.

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Step 17.2.1

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

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

Step 17.2.2

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

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

Step 17.2.3

Cancel the common factor.

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

Step 17.2.4

Rewrite the expression.

$\frac{3 x}{1} + \frac{6 x}{2 x} + \frac{- 3}{2 x}$

Step 17.2.5

Divide $3 x$ by $1$ .

$3 x + \frac{6 x}{2 x} + \frac{- 3}{2 x}$

Step 18

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

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Step 18.1

Factor $2$ out of $6 x$ .

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

Step 18.2

Cancel the common factors.

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Step 18.2.1

Factor $2$ out of $2 x$ .

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

Step 18.2.2

Cancel the common factor.

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

Step 18.2.3

Rewrite the expression.

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

Step 19

Cancel the common factor of $x$ .

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Step 19.1

Cancel the common factor.

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

Step 19.2

Divide $3$ by $1$ .

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

Step 20

Move the negative in front of the fraction.

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