Pre-Algebra Examples

$\frac{72 x^{4} - 6 x^{3} + x^{2} - 12}{12}$

Step 1

Split the fraction $\frac{72 x^{4} - 6 x^{3} + x^{2} - 12}{12}$ into two fractions.

$\frac{72 x^{4} - 6 x^{3} + x^{2}}{12} + \frac{- 12}{12}$

Step 2

Split the fraction $\frac{72 x^{4} - 6 x^{3} + x^{2}}{12}$ into two fractions.

$\frac{72 x^{4} - 6 x^{3}}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 3

Split the fraction $\frac{72 x^{4} - 6 x^{3}}{12}$ into two fractions.

$\frac{72 x^{4}}{12} + \frac{- 6 x^{3}}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 4

Cancel the common factor of $72$ and $12$ .

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Step 4.1

Factor $12$ out of $72 x^{4}$ .

$\frac{12 (6 x^{4})}{12} + \frac{- 6 x^{3}}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $12$ out of $12$ .

$\frac{12 (6 x^{4})}{12 (1)} + \frac{- 6 x^{3}}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 4.2.2

Cancel the common factor.

$\frac{12 (6 x^{4})}{12 \cdot 1} + \frac{- 6 x^{3}}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 4.2.3

Rewrite the expression.

$\frac{6 x^{4}}{1} + \frac{- 6 x^{3}}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 4.2.4

Divide $6 x^{4}$ by $1$ .

$6 x^{4} + \frac{- 6 x^{3}}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 5

Cancel the common factor of $- 6$ and $12$ .

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Step 5.1

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

$6 x^{4} + \frac{6 (- x^{3})}{12} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $6$ out of $12$ .

$6 x^{4} + \frac{6 (- x^{3})}{6 (2)} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 5.2.2

Cancel the common factor.

$6 x^{4} + \frac{6 (- x^{3})}{6 \cdot 2} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 5.2.3

Rewrite the expression.

$6 x^{4} + \frac{- x^{3}}{2} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 6

Move the negative in front of the fraction.

$6 x^{4} - \frac{x^{3}}{2} + \frac{x^{2}}{12} + \frac{- 12}{12}$

Step 7

Divide $- 12$ by $12$ .

$6 x^{4} - \frac{x^{3}}{2} + \frac{x^{2}}{12} - 1$