Pre-Algebra Examples

$(- 14 s^{4} t^{2} + 7 s^{2} t^{2} - 18 t) \div 2 s^{2} t$

Step 1

Rewrite the division as a fraction.

$\frac{- 14 s^{4} t^{2} + 7 s^{2} t^{2} - 18 t}{2 s^{2} t}$

Step 2

Factor $t$ out of $- 14 s^{4} t^{2} + 7 s^{2} t^{2} - 18 t$ .

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Step 2.1

Factor $t$ out of $- 14 s^{4} t^{2}$ .

$\frac{t (- 14 s^{4} t) + 7 s^{2} t^{2} - 18 t}{2 s^{2} t}$

Step 2.2

Factor $t$ out of $7 s^{2} t^{2}$ .

$\frac{t (- 14 s^{4} t) + t (7 s^{2} t) - 18 t}{2 s^{2} t}$

Step 2.3

Factor $t$ out of $- 18 t$ .

$\frac{t (- 14 s^{4} t) + t (7 s^{2} t) + t \cdot - 18}{2 s^{2} t}$

Step 2.4

Factor $t$ out of $t (- 14 s^{4} t) + t (7 s^{2} t)$ .

$\frac{t (- 14 s^{4} t + 7 s^{2} t) + t \cdot - 18}{2 s^{2} t}$

Step 2.5

Factor $t$ out of $t (- 14 s^{4} t + 7 s^{2} t) + t \cdot - 18$ .

$\frac{t (- 14 s^{4} t + 7 s^{2} t - 18)}{2 s^{2} t}$

Step 3

Cancel the common factor of $t$ .

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Step 3.1

Cancel the common factor.

$\frac{t (- 14 s^{4} t + 7 s^{2} t - 18)}{2 s^{2} t}$

Step 3.2

Rewrite the expression.

$\frac{- 14 s^{4} t + 7 s^{2} t - 18}{2 s^{2}}$

Step 4

Factor $- 1$ out of $- 14 s^{4} t$ .

$\frac{- (14 s^{4} t) + 7 s^{2} t - 18}{2 s^{2}}$

Step 5

Factor $- 1$ out of $7 s^{2} t$ .

$\frac{- (14 s^{4} t) - (- 7 s^{2} t) - 18}{2 s^{2}}$

Step 6

Factor $- 1$ out of $- (14 s^{4} t) - (- 7 s^{2} t)$ .

$\frac{- (14 s^{4} t - 7 s^{2} t) - 18}{2 s^{2}}$

Step 7

Rewrite $- 18$ as $- 1 (18)$ .

$\frac{- (14 s^{4} t - 7 s^{2} t) - 1 (18)}{2 s^{2}}$

Step 8

Factor $- 1$ out of $- (14 s^{4} t - 7 s^{2} t) - 1 (18)$ .

$\frac{- (14 s^{4} t - 7 s^{2} t + 18)}{2 s^{2}}$

Step 9

Rewrite $- (14 s^{4} t - 7 s^{2} t + 18)$ as $- 1 (14 s^{4} t - 7 s^{2} t + 18)$ .

$\frac{- 1 (14 s^{4} t - 7 s^{2} t + 18)}{2 s^{2}}$

Step 10

Move the negative in front of the fraction.

$- \frac{14 s^{4} t - 7 s^{2} t + 18}{2 s^{2}}$

Step 11

Split the fraction $\frac{14 s^{4} t - 7 s^{2} t + 18}{2 s^{2}}$ into two fractions.

$- (\frac{14 s^{4} t - 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 12

Split the fraction $\frac{14 s^{4} t - 7 s^{2} t}{2 s^{2}}$ into two fractions.

$- (\frac{14 s^{4} t}{2 s^{2}} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 13

Cancel the common factor of $14$ and $2$ .

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Step 13.1

Factor $2$ out of $14 s^{4} t$ .

$- (\frac{2 (7 s^{4} t)}{2 s^{2}} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 13.2

Cancel the common factors.

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Step 13.2.1

Factor $2$ out of $2 s^{2}$ .

$- (\frac{2 (7 s^{4} t)}{2 (s^{2})} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 13.2.2

Cancel the common factor.

$- (\frac{2 (7 s^{4} t)}{2 s^{2}} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 13.2.3

Rewrite the expression.

$- (\frac{7 s^{4} t}{s^{2}} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 14

Cancel the common factor of $s^{4}$ and $s^{2}$ .

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Step 14.1

Factor $s^{2}$ out of $7 s^{4} t$ .

$- (\frac{s^{2} (7 s^{2} t)}{s^{2}} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Multiply by $1$ .

$- (\frac{s^{2} (7 s^{2} t)}{s^{2} \cdot 1} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 14.2.2

Cancel the common factor.

$- (\frac{s^{2} (7 s^{2} t)}{s^{2} \cdot 1} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 14.2.3

Rewrite the expression.

$- (\frac{7 s^{2} t}{1} + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 14.2.4

Divide $7 s^{2} t$ by $1$ .

$- (7 s^{2} t + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 15

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

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Step 15.1

Cancel the common factor.

$- (7 s^{2} t + \frac{- 7 s^{2} t}{2 s^{2}} + \frac{18}{2 s^{2}})$

Step 15.2

Rewrite the expression.

$- (7 s^{2} t + \frac{- 7 t}{2} + \frac{18}{2 s^{2}})$

Step 16

Move the negative in front of the fraction.

$- (7 s^{2} t - \frac{7 t}{2} + \frac{18}{2 s^{2}})$

Step 17

Cancel the common factor of $18$ and $2$ .

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Step 17.1

Factor $2$ out of $18$ .

$- (7 s^{2} t - \frac{7 t}{2} + \frac{2 \cdot 9}{2 s^{2}})$

Step 17.2

Cancel the common factors.

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Step 17.2.1

Factor $2$ out of $2 s^{2}$ .

$- (7 s^{2} t - \frac{7 t}{2} + \frac{2 \cdot 9}{2 (s^{2})})$

Step 17.2.2

Cancel the common factor.

$- (7 s^{2} t - \frac{7 t}{2} + \frac{2 \cdot 9}{2 s^{2}})$

Step 17.2.3

Rewrite the expression.

$- (7 s^{2} t - \frac{7 t}{2} + \frac{9}{s^{2}})$