Pre-Algebra Examples

$\frac{42 x^{2} + 18 x - 13}{6 x}$

Step 1

Split the fraction $\frac{42 x^{2} + 18 x - 13}{6 x}$ into two fractions.

$\frac{42 x^{2} + 18 x}{6 x} + \frac{- 13}{6 x}$

Step 2

Split the fraction $\frac{42 x^{2} + 18 x}{6 x}$ into two fractions.

$\frac{42 x^{2}}{6 x} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 3

Cancel the common factor of $42$ and $6$ .

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Step 3.1

Factor $6$ out of $42 x^{2}$ .

$\frac{6 (7 x^{2})}{6 x} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $6$ out of $6 x$ .

$\frac{6 (7 x^{2})}{6 (x)} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 3.2.2

Cancel the common factor.

$\frac{6 (7 x^{2})}{6 x} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 3.2.3

Rewrite the expression.

$\frac{7 x^{2}}{x} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 4

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

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Step 4.1

Factor $x$ out of $7 x^{2}$ .

$\frac{x (7 x)}{x} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{x (7 x)}{x^{1}} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 4.2.2

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

$\frac{x (7 x)}{x \cdot 1} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 4.2.3

Cancel the common factor.

$\frac{x (7 x)}{x \cdot 1} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 4.2.4

Rewrite the expression.

$\frac{7 x}{1} + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 4.2.5

Divide $7 x$ by $1$ .

$7 x + \frac{18 x}{6 x} + \frac{- 13}{6 x}$

Step 5

Cancel the common factor of $18$ and $6$ .

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Step 5.1

Factor $6$ out of $18 x$ .

$7 x + \frac{6 (3 x)}{6 x} + \frac{- 13}{6 x}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $6$ out of $6 x$ .

$7 x + \frac{6 (3 x)}{6 (x)} + \frac{- 13}{6 x}$

Step 5.2.2

Cancel the common factor.

$7 x + \frac{6 (3 x)}{6 x} + \frac{- 13}{6 x}$

Step 5.2.3

Rewrite the expression.

$7 x + \frac{3 x}{x} + \frac{- 13}{6 x}$

Step 6

Cancel the common factor of $x$ .

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Step 6.1

Cancel the common factor.

$7 x + \frac{3 x}{x} + \frac{- 13}{6 x}$

Step 6.2

Divide $3$ by $1$ .

$7 x + 3 + \frac{- 13}{6 x}$

Step 7

Move the negative in front of the fraction.

$7 x + 3 - \frac{13}{6 x}$