Pre-Algebra Examples

$\frac{33 r^{4} - 21 r^{3} - 3 r^{2} + 12 r - 5}{3 r}$

Step 1

Split the fraction $\frac{33 r^{4} - 21 r^{3} - 3 r^{2} + 12 r - 5}{3 r}$ into two fractions.

$\frac{33 r^{4} - 21 r^{3} - 3 r^{2} + 12 r}{3 r} + \frac{- 5}{3 r}$

Step 2

Split the fraction $\frac{33 r^{4} - 21 r^{3} - 3 r^{2} + 12 r}{3 r}$ into two fractions.

$\frac{33 r^{4} - 21 r^{3} - 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 3

Split the fraction $\frac{33 r^{4} - 21 r^{3} - 3 r^{2}}{3 r}$ into two fractions.

$\frac{33 r^{4} - 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 4

Split the fraction $\frac{33 r^{4} - 21 r^{3}}{3 r}$ into two fractions.

$\frac{33 r^{4}}{3 r} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 5

Cancel the common factor of $33$ and $3$ .

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Step 5.1

Factor $3$ out of $33 r^{4}$ .

$\frac{3 (11 r^{4})}{3 r} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $3 r$ .

$\frac{3 (11 r^{4})}{3 (r)} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (11 r^{4})}{3 r} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 5.2.3

Rewrite the expression.

$\frac{11 r^{4}}{r} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 6

Cancel the common factor of $r^{4}$ and $r$ .

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Step 6.1

Factor $r$ out of $11 r^{4}$ .

$\frac{r (11 r^{3})}{r} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{r (11 r^{3})}{r^{1}} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 6.2.2

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

$\frac{r (11 r^{3})}{r \cdot 1} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 6.2.3

Cancel the common factor.

$\frac{r (11 r^{3})}{r \cdot 1} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 6.2.4

Rewrite the expression.

$\frac{11 r^{3}}{1} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 6.2.5

Divide $11 r^{3}$ by $1$ .

$11 r^{3} + \frac{- 21 r^{3}}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 7

Cancel the common factor of $- 21$ and $3$ .

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Step 7.1

Factor $3$ out of $- 21 r^{3}$ .

$11 r^{3} + \frac{3 (- 7 r^{3})}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $3 r$ .

$11 r^{3} + \frac{3 (- 7 r^{3})}{3 (r)} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 7.2.2

Cancel the common factor.

$11 r^{3} + \frac{3 (- 7 r^{3})}{3 r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 7.2.3

Rewrite the expression.

$11 r^{3} + \frac{- 7 r^{3}}{r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 8

Cancel the common factor of $r^{3}$ and $r$ .

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Step 8.1

Factor $r$ out of $- 7 r^{3}$ .

$11 r^{3} + \frac{r (- 7 r^{2})}{r} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

$11 r^{3} + \frac{r (- 7 r^{2})}{r^{1}} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 8.2.2

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

$11 r^{3} + \frac{r (- 7 r^{2})}{r \cdot 1} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 8.2.3

Cancel the common factor.

$11 r^{3} + \frac{r (- 7 r^{2})}{r \cdot 1} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 8.2.4

Rewrite the expression.

$11 r^{3} + \frac{- 7 r^{2}}{1} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 8.2.5

Divide $- 7 r^{2}$ by $1$ .

$11 r^{3} - 7 r^{2} + \frac{- 3 r^{2}}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 9

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

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Step 9.1

Factor $3$ out of $- 3 r^{2}$ .

$11 r^{3} - 7 r^{2} + \frac{3 (- r^{2})}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $3 r$ .

$11 r^{3} - 7 r^{2} + \frac{3 (- r^{2})}{3 (r)} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 9.2.2

Cancel the common factor.

$11 r^{3} - 7 r^{2} + \frac{3 (- r^{2})}{3 r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 9.2.3

Rewrite the expression.

$11 r^{3} - 7 r^{2} + \frac{- r^{2}}{r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 10

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

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Step 10.1

Factor $r$ out of $- r^{2}$ .

$11 r^{3} - 7 r^{2} + \frac{r (- r)}{r} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

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

$11 r^{3} - 7 r^{2} + \frac{r (- r)}{r^{1}} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 10.2.2

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

$11 r^{3} - 7 r^{2} + \frac{r (- r)}{r \cdot 1} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 10.2.3

Cancel the common factor.

$11 r^{3} - 7 r^{2} + \frac{r (- r)}{r \cdot 1} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 10.2.4

Rewrite the expression.

$11 r^{3} - 7 r^{2} + \frac{- r}{1} + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 10.2.5

Divide $- r$ by $1$ .

$11 r^{3} - 7 r^{2} - r + \frac{12 r}{3 r} + \frac{- 5}{3 r}$

Step 11

Cancel the common factor of $12$ and $3$ .

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Step 11.1

Factor $3$ out of $12 r$ .

$11 r^{3} - 7 r^{2} - r + \frac{3 (4 r)}{3 r} + \frac{- 5}{3 r}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $3$ out of $3 r$ .

$11 r^{3} - 7 r^{2} - r + \frac{3 (4 r)}{3 (r)} + \frac{- 5}{3 r}$

Step 11.2.2

Cancel the common factor.

$11 r^{3} - 7 r^{2} - r + \frac{3 (4 r)}{3 r} + \frac{- 5}{3 r}$

Step 11.2.3

Rewrite the expression.

$11 r^{3} - 7 r^{2} - r + \frac{4 r}{r} + \frac{- 5}{3 r}$

Step 12

Cancel the common factor of $r$ .

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Step 12.1

Cancel the common factor.

$11 r^{3} - 7 r^{2} - r + \frac{4 r}{r} + \frac{- 5}{3 r}$

Step 12.2

Divide $4$ by $1$ .

$11 r^{3} - 7 r^{2} - r + 4 + \frac{- 5}{3 r}$

Step 13

Move the negative in front of the fraction.

$11 r^{3} - 7 r^{2} - r + 4 - \frac{5}{3 r}$