Pre-Algebra Examples

$\frac{12 x^{9} + 16 x^{7} + 20}{12 x^{6}}$

Step 1

Cancel the common factor of $12 x^{9} + 16 x^{7} + 20$ and $12$ .

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Step 1.1

Factor $4$ out of $12 x^{9}$ .

$\frac{4 (3 x^{9}) + 16 x^{7} + 20}{12 x^{6}}$

Step 1.2

Factor $4$ out of $16 x^{7}$ .

$\frac{4 (3 x^{9}) + 4 (4 x^{7}) + 20}{12 x^{6}}$

Step 1.3

Factor $4$ out of $4 (3 x^{9}) + 4 (4 x^{7})$ .

$\frac{4 (3 x^{9} + 4 x^{7}) + 20}{12 x^{6}}$

Step 1.4

Factor $4$ out of $20$ .

$\frac{4 (3 x^{9} + 4 x^{7}) + 4 (5)}{12 x^{6}}$

Step 1.5

Factor $4$ out of $4 (3 x^{9} + 4 x^{7}) + 4 (5)$ .

$\frac{4 (3 x^{9} + 4 x^{7} + 5)}{12 x^{6}}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $4$ out of $12 x^{6}$ .

$\frac{4 (3 x^{9} + 4 x^{7} + 5)}{4 (3 x^{6})}$

Step 1.6.2

Cancel the common factor.

$\frac{4 (3 x^{9} + 4 x^{7} + 5)}{4 (3 x^{6})}$

Step 1.6.3

Rewrite the expression.

$\frac{3 x^{9} + 4 x^{7} + 5}{3 x^{6}}$

Step 2

Split the fraction $\frac{3 x^{9} + 4 x^{7} + 5}{3 x^{6}}$ into two fractions.

$\frac{3 x^{9} + 4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 3

Split the fraction $\frac{3 x^{9} + 4 x^{7}}{3 x^{6}}$ into two fractions.

$\frac{3 x^{9}}{3 x^{6}} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$\frac{3 x^{9}}{3 x^{6}} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 4.2

Rewrite the expression.

$\frac{x^{9}}{x^{6}} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 5

Cancel the common factor of $x^{9}$ and $x^{6}$ .

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Step 5.1

Factor $x^{6}$ out of $x^{9}$ .

$\frac{x^{6} x^{3}}{x^{6}} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$\frac{x^{6} x^{3}}{x^{6} \cdot 1} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 5.2.2

Cancel the common factor.

$\frac{x^{6} x^{3}}{x^{6} \cdot 1} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 5.2.3

Rewrite the expression.

$\frac{x^{3}}{1} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 5.2.4

Divide $x^{3}$ by $1$ .

$x^{3} + \frac{4 x^{7}}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 6

Cancel the common factor of $x^{7}$ and $x^{6}$ .

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Step 6.1

Factor $x^{6}$ out of $4 x^{7}$ .

$x^{3} + \frac{x^{6} (4 x)}{3 x^{6}} + \frac{5}{3 x^{6}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$x^{3} + \frac{x^{6} (4 x)}{x^{6} \cdot 3} + \frac{5}{3 x^{6}}$

Step 6.2.2

Cancel the common factor.

$x^{3} + \frac{x^{6} (4 x)}{x^{6} \cdot 3} + \frac{5}{3 x^{6}}$

Step 6.2.3

Rewrite the expression.

$x^{3} + \frac{4 x}{3} + \frac{5}{3 x^{6}}$