Pre-Algebra Examples

$\frac{- 8 r^{4} + 30 r^{3} - 22 r^{2} + 19 r + 29}{- 2 r}$

Step 1

Move the negative in front of the fraction.

$- \frac{- 8 r^{4} + 30 r^{3} - 22 r^{2} + 19 r + 29}{2 r}$

Step 2

Factor $- 1$ out of $- 8 r^{4}$ .

$- \frac{- (8 r^{4}) + 30 r^{3} - 22 r^{2} + 19 r + 29}{2 r}$

Step 3

Factor $- 1$ out of $30 r^{3}$ .

$- \frac{- (8 r^{4}) - (- 30 r^{3}) - 22 r^{2} + 19 r + 29}{2 r}$

Step 4

Factor $- 1$ out of $- (8 r^{4}) - (- 30 r^{3})$ .

$- \frac{- (8 r^{4} - 30 r^{3}) - 22 r^{2} + 19 r + 29}{2 r}$

Step 5

Factor $- 1$ out of $- 22 r^{2}$ .

$- \frac{- (8 r^{4} - 30 r^{3}) - (22 r^{2}) + 19 r + 29}{2 r}$

Step 6

Factor $- 1$ out of $- (8 r^{4} - 30 r^{3}) - (22 r^{2})$ .

$- \frac{- (8 r^{4} - 30 r^{3} + 22 r^{2}) + 19 r + 29}{2 r}$

Step 7

Factor $- 1$ out of $19 r$ .

$- \frac{- (8 r^{4} - 30 r^{3} + 22 r^{2}) - (- 19 r) + 29}{2 r}$

Step 8

Factor $- 1$ out of $- (8 r^{4} - 30 r^{3} + 22 r^{2}) - (- 19 r)$ .

$- \frac{- (8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r) + 29}{2 r}$

Step 9

Rewrite $29$ as $- 1 (- 29)$ .

$- \frac{- (8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r) - 1 (- 29)}{2 r}$

Step 10

Factor $- 1$ out of $- (8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r) - 1 (- 29)$ .

$- \frac{- (8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29)}{2 r}$

Step 11

Rewrite $- (8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29)$ as $- 1 (8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29)$ .

$- \frac{- 1 (8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29)}{2 r}$

Step 12

Move the negative in front of the fraction.

$- - \frac{8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29}{2 r}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \frac{8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29}{2 r}$

Step 14

Multiply $\frac{8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29}{2 r}$ by $1$ .

$\frac{8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29}{2 r}$

Step 15

Split the fraction $\frac{8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r - 29}{2 r}$ into two fractions.

$\frac{8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r}{2 r} + \frac{- 29}{2 r}$

Step 16

Split the fraction $\frac{8 r^{4} - 30 r^{3} + 22 r^{2} - 19 r}{2 r}$ into two fractions.

$\frac{8 r^{4} - 30 r^{3} + 22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 17

Split the fraction $\frac{8 r^{4} - 30 r^{3} + 22 r^{2}}{2 r}$ into two fractions.

$\frac{8 r^{4} - 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 18

Split the fraction $\frac{8 r^{4} - 30 r^{3}}{2 r}$ into two fractions.

$\frac{8 r^{4}}{2 r} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 19

Cancel the common factor of $8$ and $2$ .

Tap for more steps...

Step 19.1

Factor $2$ out of $8 r^{4}$ .

$\frac{2 (4 r^{4})}{2 r} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 19.2

Cancel the common factors.

Tap for more steps...

Step 19.2.1

Factor $2$ out of $2 r$ .

$\frac{2 (4 r^{4})}{2 (r)} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 19.2.2

Cancel the common factor.

$\frac{2 (4 r^{4})}{2 r} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 19.2.3

Rewrite the expression.

$\frac{4 r^{4}}{r} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 20

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

Tap for more steps...

Step 20.1

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

$\frac{r (4 r^{3})}{r} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 20.2

Cancel the common factors.

Tap for more steps...

Step 20.2.1

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

$\frac{r (4 r^{3})}{r^{1}} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 20.2.2

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

$\frac{r (4 r^{3})}{r \cdot 1} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 20.2.3

Cancel the common factor.

$\frac{r (4 r^{3})}{r \cdot 1} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 20.2.4

Rewrite the expression.

$\frac{4 r^{3}}{1} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 20.2.5

Divide $4 r^{3}$ by $1$ .

$4 r^{3} + \frac{- 30 r^{3}}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 21

Cancel the common factor of $- 30$ and $2$ .

Tap for more steps...

Step 21.1

Factor $2$ out of $- 30 r^{3}$ .

$4 r^{3} + \frac{2 (- 15 r^{3})}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 21.2

Cancel the common factors.

Tap for more steps...

Step 21.2.1

Factor $2$ out of $2 r$ .

$4 r^{3} + \frac{2 (- 15 r^{3})}{2 (r)} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 21.2.2

Cancel the common factor.

$4 r^{3} + \frac{2 (- 15 r^{3})}{2 r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 21.2.3

Rewrite the expression.

$4 r^{3} + \frac{- 15 r^{3}}{r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 22

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

Tap for more steps...

Step 22.1

Factor $r$ out of $- 15 r^{3}$ .

$4 r^{3} + \frac{r (- 15 r^{2})}{r} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 22.2

Cancel the common factors.

Tap for more steps...

Step 22.2.1

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

$4 r^{3} + \frac{r (- 15 r^{2})}{r^{1}} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 22.2.2

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

$4 r^{3} + \frac{r (- 15 r^{2})}{r \cdot 1} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 22.2.3

Cancel the common factor.

$4 r^{3} + \frac{r (- 15 r^{2})}{r \cdot 1} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 22.2.4

Rewrite the expression.

$4 r^{3} + \frac{- 15 r^{2}}{1} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 22.2.5

Divide $- 15 r^{2}$ by $1$ .

$4 r^{3} - 15 r^{2} + \frac{22 r^{2}}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 23

Cancel the common factor of $22$ and $2$ .

Tap for more steps...

Step 23.1

Factor $2$ out of $22 r^{2}$ .

$4 r^{3} - 15 r^{2} + \frac{2 (11 r^{2})}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 23.2

Cancel the common factors.

Tap for more steps...

Step 23.2.1

Factor $2$ out of $2 r$ .

$4 r^{3} - 15 r^{2} + \frac{2 (11 r^{2})}{2 (r)} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 23.2.2

Cancel the common factor.

$4 r^{3} - 15 r^{2} + \frac{2 (11 r^{2})}{2 r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 23.2.3

Rewrite the expression.

$4 r^{3} - 15 r^{2} + \frac{11 r^{2}}{r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 24

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

Tap for more steps...

Step 24.1

Factor $r$ out of $11 r^{2}$ .

$4 r^{3} - 15 r^{2} + \frac{r (11 r)}{r} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 24.2

Cancel the common factors.

Tap for more steps...

Step 24.2.1

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

$4 r^{3} - 15 r^{2} + \frac{r (11 r)}{r^{1}} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 24.2.2

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

$4 r^{3} - 15 r^{2} + \frac{r (11 r)}{r \cdot 1} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 24.2.3

Cancel the common factor.

$4 r^{3} - 15 r^{2} + \frac{r (11 r)}{r \cdot 1} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 24.2.4

Rewrite the expression.

$4 r^{3} - 15 r^{2} + \frac{11 r}{1} + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 24.2.5

Divide $11 r$ by $1$ .

$4 r^{3} - 15 r^{2} + 11 r + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 25

Cancel the common factor of $r$ .

Tap for more steps...

Step 25.1

Cancel the common factor.

$4 r^{3} - 15 r^{2} + 11 r + \frac{- 19 r}{2 r} + \frac{- 29}{2 r}$

Step 25.2

Rewrite the expression.

$4 r^{3} - 15 r^{2} + 11 r + \frac{- 19}{2} + \frac{- 29}{2 r}$

Step 26

Move the negative in front of the fraction.

$4 r^{3} - 15 r^{2} + 11 r - \frac{19}{2} + \frac{- 29}{2 r}$

Step 27

Move the negative in front of the fraction.

$4 r^{3} - 15 r^{2} + 11 r - \frac{19}{2} - \frac{29}{2 r}$