Pre-Algebra Examples

$(- 15 z^{2} v + 23 z^{3} v^{2}) \div (- 3 z^{3} v^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{- 15 z^{2} v + 23 z^{3} v^{2}}{- 3 z^{3} v^{2}}$

Step 2

Factor $z^{2} v$ out of $- 15 z^{2} v + 23 z^{3} v^{2}$ .

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Step 2.1

Factor $z^{2} v$ out of $- 15 z^{2} v$ .

$\frac{z^{2} v (- 15) + 23 z^{3} v^{2}}{- 3 z^{3} v^{2}}$

Step 2.2

Factor $z^{2} v$ out of $23 z^{3} v^{2}$ .

$\frac{z^{2} v (- 15) + z^{2} v (23 z v)}{- 3 z^{3} v^{2}}$

Step 2.3

Factor $z^{2} v$ out of $z^{2} v (- 15) + z^{2} v (23 z v)$ .

$\frac{z^{2} v (- 15 + 23 z v)}{- 3 z^{3} v^{2}}$

Step 3

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

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Step 3.1

Factor $z^{2}$ out of $z^{2} v (- 15 + 23 z v)$ .

$\frac{z^{2} (v (- 15 + 23 z v))}{- 3 z^{3} v^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $z^{2}$ out of $- 3 z^{3} v^{2}$ .

$\frac{z^{2} (v (- 15 + 23 z v))}{z^{2} (- 3 z v^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{z^{2} (v (- 15 + 23 z v))}{z^{2} (- 3 z v^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{v (- 15 + 23 z v)}{- 3 z v^{2}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $v$ out of $- 3 z v^{2}$ .

$\frac{v (- 15 + 23 z v)}{v (- 3 z v)}$

Step 4.2

Cancel the common factor.

$\frac{v (- 15 + 23 z v)}{v (- 3 z v)}$

Step 4.3

Rewrite the expression.

$\frac{- 15 + 23 z v}{- 3 z v}$

Step 5

Move the negative in front of the fraction.

$- \frac{- 15 + 23 z v}{3 z v}$

Step 6

Rewrite $- 15$ as $- 1 (15)$ .

$- \frac{- 1 (15) + 23 z v}{3 z v}$

Step 7

Factor $- 1$ out of $23 z v$ .

$- \frac{- 1 (15) - (- 23 z v)}{3 z v}$

Step 8

Factor $- 1$ out of $- 1 (15) - (- 23 z v)$ .

$- \frac{- 1 (15 - 23 z v)}{3 z v}$

Step 9

Simplify the expression.

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Step 9.1

Move the negative in front of the fraction.

$- - \frac{15 - 23 z v}{3 z v}$

Step 9.2

Multiply $- 1$ by $- 1$ .

$1 \frac{15 - 23 z v}{3 z v}$

Step 9.3

Multiply $\frac{15 - 23 z v}{3 z v}$ by $1$ .

$\frac{15 - 23 z v}{3 z v}$