Algebra Examples

$(- 6 w^{3} z^{4} - 3 w^{2} z^{5} + 4 w + 5 z) \div (2 w^{2} z)$

Step 1

Rewrite the division as a fraction.

$\frac{- 6 w^{3} z^{4} - 3 w^{2} z^{5} + 4 w + 5 z}{2 w^{2} z}$

Step 2

Factor $- 1$ out of $- 6 w^{3} z^{4}$ .

$\frac{- (6 w^{3} z^{4}) - 3 w^{2} z^{5} + 4 w + 5 z}{2 w^{2} z}$

Step 3

Factor $- 1$ out of $- 3 w^{2} z^{5}$ .

$\frac{- (6 w^{3} z^{4}) - (3 w^{2} z^{5}) + 4 w + 5 z}{2 w^{2} z}$

Step 4

Factor $- 1$ out of $- (6 w^{3} z^{4}) - (3 w^{2} z^{5})$ .

$\frac{- (6 w^{3} z^{4} + 3 w^{2} z^{5}) + 4 w + 5 z}{2 w^{2} z}$

Step 5

Factor $- 1$ out of $4 w$ .

$\frac{- (6 w^{3} z^{4} + 3 w^{2} z^{5}) - (- 4 w) + 5 z}{2 w^{2} z}$

Step 6

Factor $- 1$ out of $- (6 w^{3} z^{4} + 3 w^{2} z^{5}) - (- 4 w)$ .

$\frac{- (6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w) + 5 z}{2 w^{2} z}$

Step 7

Factor $- 1$ out of $5 z$ .

$\frac{- (6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w) - (- 5 z)}{2 w^{2} z}$

Step 8

Factor $- 1$ out of $- (6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w) - (- 5 z)$ .

$\frac{- (6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w - 5 z)}{2 w^{2} z}$

Step 9

Rewrite $- (6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w - 5 z)$ as $- 1 (6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w - 5 z)$ .

$\frac{- 1 (6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w - 5 z)}{2 w^{2} z}$

Step 10

Move the negative in front of the fraction.

$- \frac{6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w - 5 z}{2 w^{2} z}$

Step 11

Split the fraction $\frac{6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w - 5 z}{2 w^{2} z}$ into two fractions.

$- (\frac{6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 12

Split the fraction $\frac{6 w^{3} z^{4} + 3 w^{2} z^{5} - 4 w}{2 w^{2} z}$ into two fractions.

$- (\frac{6 w^{3} z^{4} + 3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 13

Split the fraction $\frac{6 w^{3} z^{4} + 3 w^{2} z^{5}}{2 w^{2} z}$ into two fractions.

$- (\frac{6 w^{3} z^{4}}{2 w^{2} z} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 14

Cancel the common factor of $6$ and $2$ .

Tap for more steps...

Step 14.1

Factor $2$ out of $6 w^{3} z^{4}$ .

$- (\frac{2 (3 w^{3} z^{4})}{2 w^{2} z} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 14.2

Cancel the common factors.

Tap for more steps...

Step 14.2.1

Factor $2$ out of $2 w^{2} z$ .

$- (\frac{2 (3 w^{3} z^{4})}{2 (w^{2} z)} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 14.2.2

Cancel the common factor.

$- (\frac{2 (3 w^{3} z^{4})}{2 (w^{2} z)} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 14.2.3

Rewrite the expression.

$- (\frac{3 w^{3} z^{4}}{w^{2} z} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 15

Cancel the common factor of $w^{3}$ and $w^{2}$ .

Tap for more steps...

Step 15.1

Factor $w^{2}$ out of $3 w^{3} z^{4}$ .

$- (\frac{w^{2} (3 w z^{4})}{w^{2} z} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 15.2

Cancel the common factors.

Tap for more steps...

Step 15.2.1

Factor $w^{2}$ out of $w^{2} z$ .

$- (\frac{w^{2} (3 w z^{4})}{w^{2} (z)} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 15.2.2

Cancel the common factor.

$- (\frac{w^{2} (3 w z^{4})}{w^{2} z} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 15.2.3

Rewrite the expression.

$- (\frac{3 w z^{4}}{z} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 16

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

Tap for more steps...

Step 16.1

Factor $z$ out of $3 w z^{4}$ .

$- (\frac{z (3 w z^{3})}{z} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 16.2

Cancel the common factors.

Tap for more steps...

Step 16.2.1

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

$- (\frac{z (3 w z^{3})}{z^{1}} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 16.2.2

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

$- (\frac{z (3 w z^{3})}{z \cdot 1} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 16.2.3

Cancel the common factor.

$- (\frac{z (3 w z^{3})}{z \cdot 1} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 16.2.4

Rewrite the expression.

$- (\frac{3 w z^{3}}{1} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 16.2.5

Divide $3 w z^{3}$ by $1$ .

$- (3 w z^{3} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 17

Cancel the common factor of $w^{2}$ .

Tap for more steps...

Step 17.1

Cancel the common factor.

$- (3 w z^{3} + \frac{3 w^{2} z^{5}}{2 w^{2} z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 17.2

Rewrite the expression.

$- (3 w z^{3} + \frac{3 z^{5}}{2 z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 18

Cancel the common factor of $z^{5}$ and $z$ .

Tap for more steps...

Step 18.1

Factor $z$ out of $3 z^{5}$ .

$- (3 w z^{3} + \frac{z (3 z^{4})}{2 z} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 18.2

Cancel the common factors.

Tap for more steps...

Step 18.2.1

Factor $z$ out of $2 z$ .

$- (3 w z^{3} + \frac{z (3 z^{4})}{z \cdot 2} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 18.2.2

Cancel the common factor.

$- (3 w z^{3} + \frac{z (3 z^{4})}{z \cdot 2} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 18.2.3

Rewrite the expression.

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{- 4 w}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 19

Cancel the common factor of $- 4$ and $2$ .

Tap for more steps...

Step 19.1

Factor $2$ out of $- 4 w$ .

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{2 (- 2 w)}{2 w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 19.2

Cancel the common factors.

Tap for more steps...

Step 19.2.1

Factor $2$ out of $2 w^{2} z$ .

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{2 (- 2 w)}{2 (w^{2} z)} + \frac{- 5 z}{2 w^{2} z})$

Step 19.2.2

Cancel the common factor.

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{2 (- 2 w)}{2 (w^{2} z)} + \frac{- 5 z}{2 w^{2} z})$

Step 19.2.3

Rewrite the expression.

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{- 2 w}{w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 20

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

Tap for more steps...

Step 20.1

Factor $w$ out of $- 2 w$ .

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{w \cdot - 2}{w^{2} z} + \frac{- 5 z}{2 w^{2} z})$

Step 20.2

Cancel the common factors.

Tap for more steps...

Step 20.2.1

Factor $w$ out of $w^{2} z$ .

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{w \cdot - 2}{w (w z)} + \frac{- 5 z}{2 w^{2} z})$

Step 20.2.2

Cancel the common factor.

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{w \cdot - 2}{w (w z)} + \frac{- 5 z}{2 w^{2} z})$

Step 20.2.3

Rewrite the expression.

$- (3 w z^{3} + \frac{3 z^{4}}{2} + \frac{- 2}{w z} + \frac{- 5 z}{2 w^{2} z})$

Step 21

Move the negative in front of the fraction.

$- (3 w z^{3} + \frac{3 z^{4}}{2} - \frac{2}{w z} + \frac{- 5 z}{2 w^{2} z})$

Step 22

Cancel the common factor of $z$ .

Tap for more steps...

Step 22.1

Cancel the common factor.

$- (3 w z^{3} + \frac{3 z^{4}}{2} - \frac{2}{w z} + \frac{- 5 z}{2 w^{2} z})$

Step 22.2

Rewrite the expression.

$- (3 w z^{3} + \frac{3 z^{4}}{2} - \frac{2}{w z} + \frac{- 5}{2 w^{2}})$

Step 23

Move the negative in front of the fraction.

$- (3 w z^{3} + \frac{3 z^{4}}{2} - \frac{2}{w z} - \frac{5}{2 w^{2}})$