Pre-Algebra Examples

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

Step 1

Factor $r^{2}$ out of $- 4 r^{5} + 7 r^{3} - 3 r^{2}$ .

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Step 1.1

Factor $r^{2}$ out of $- 4 r^{5}$ .

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

Step 1.2

Factor $r^{2}$ out of $7 r^{3}$ .

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

Step 1.3

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

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

Step 1.4

Factor $r^{2}$ out of $r^{2} (- 4 r^{3}) + r^{2} (7 r)$ .

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

Step 1.5

Factor $r^{2}$ out of $r^{2} (- 4 r^{3} + 7 r) + r^{2} \cdot - 3$ .

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

Step 2

Cancel the common factors.

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Step 2.1

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

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Factor $- 1$ out of $- 4 r^{3}$ .

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

Step 5

Factor $- 1$ out of $7 r$ .

$- \frac{- (4 r^{3}) - (- 7 r) - 3}{r}$

Step 6

Factor $- 1$ out of $- (4 r^{3}) - (- 7 r)$ .

$- \frac{- (4 r^{3} - 7 r) - 3}{r}$

Step 7

Rewrite $- 3$ as $- 1 (3)$ .

$- \frac{- (4 r^{3} - 7 r) - 1 (3)}{r}$

Step 8

Factor $- 1$ out of $- (4 r^{3} - 7 r) - 1 (3)$ .

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

Step 9

Rewrite $- (4 r^{3} - 7 r + 3)$ as $- 1 (4 r^{3} - 7 r + 3)$ .

$- \frac{- 1 (4 r^{3} - 7 r + 3)}{r}$

Step 10

Move the negative in front of the fraction.

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

Step 11

Multiply $- 1$ by $- 1$ .

$1 \frac{4 r^{3} - 7 r + 3}{r}$

Step 12

Multiply $\frac{4 r^{3} - 7 r + 3}{r}$ by $1$ .

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

Step 13

Split the fraction $\frac{4 r^{3} - 7 r + 3}{r}$ into two fractions.

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

Step 14

Split the fraction $\frac{4 r^{3} - 7 r}{r}$ into two fractions.

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

Step 15

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

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Step 15.1

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

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

Step 15.2

Cancel the common factors.

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Step 15.2.1

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

$\frac{r (4 r^{2})}{r^{1}} + \frac{- 7 r}{r} + \frac{3}{r}$

Step 15.2.2

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

$\frac{r (4 r^{2})}{r \cdot 1} + \frac{- 7 r}{r} + \frac{3}{r}$

Step 15.2.3

Cancel the common factor.

$\frac{r (4 r^{2})}{r \cdot 1} + \frac{- 7 r}{r} + \frac{3}{r}$

Step 15.2.4

Rewrite the expression.

$\frac{4 r^{2}}{1} + \frac{- 7 r}{r} + \frac{3}{r}$

Step 15.2.5

Divide $4 r^{2}$ by $1$ .

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

Step 16

Cancel the common factor of $r$ .

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Step 16.1

Cancel the common factor.

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

Step 16.2

Divide $- 7$ by $1$ .

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