Algebra Examples

$(- 30 x^{2} y^{2} - 45 x^{2} y^{3} z) \div (- 15 x^{2} y^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{- 30 x^{2} y^{2} - 45 x^{2} y^{3} z}{- 15 x^{2} y^{3}}$

Step 2

Factor $15 x^{2} y^{2}$ out of $- 30 x^{2} y^{2} - 45 x^{2} y^{3} z$ .

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Step 2.1

Factor $15 x^{2} y^{2}$ out of $- 30 x^{2} y^{2}$ .

$\frac{15 x^{2} y^{2} (- 2) - 45 x^{2} y^{3} z}{- 15 x^{2} y^{3}}$

Step 2.2

Factor $15 x^{2} y^{2}$ out of $- 45 x^{2} y^{3} z$ .

$\frac{15 x^{2} y^{2} (- 2) + 15 x^{2} y^{2} (- 3 y z)}{- 15 x^{2} y^{3}}$

Step 2.3

Factor $15 x^{2} y^{2}$ out of $15 x^{2} y^{2} (- 2) + 15 x^{2} y^{2} (- 3 y z)$ .

$\frac{15 x^{2} y^{2} (- 2 - 3 y z)}{- 15 x^{2} y^{3}}$

Step 3

Cancel the common factor of $15$ and $- 15$ .

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Step 3.1

Factor $15$ out of $15 x^{2} y^{2} (- 2 - 3 y z)$ .

$\frac{15 (x^{2} y^{2} (- 2 - 3 y z))}{- 15 x^{2} y^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $15$ out of $- 15 x^{2} y^{3}$ .

$\frac{15 (x^{2} y^{2} (- 2 - 3 y z))}{15 (- x^{2} y^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{15 (x^{2} y^{2} (- 2 - 3 y z))}{15 (- x^{2} y^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{2} y^{2} (- 2 - 3 y z)}{- x^{2} y^{3}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{x^{2} y^{2} (- 2 - 3 y z)}{- x^{2} y^{3}}$

Step 4.2

Rewrite the expression.

$\frac{y^{2} (- 2 - 3 y z)}{- 1 y^{3}}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $y^{2}$ out of $- 1 y^{3}$ .

$\frac{y^{2} (- 2 - 3 y z)}{y^{2} (- 1 y)}$

Step 5.2

Cancel the common factor.

$\frac{y^{2} (- 2 - 3 y z)}{y^{2} (- 1 y)}$

Step 5.3

Rewrite the expression.

$\frac{- 2 - 3 y z}{- 1 y}$

Step 6

Move the negative in front of the fraction.

$- \frac{- 2 - 3 y z}{y}$

Step 7

Rewrite $- 2$ as $- 1 (2)$ .

$- \frac{- 1 (2) - 3 y z}{y}$

Step 8

Factor $- 1$ out of $- 3 y z$ .

$- \frac{- 1 (2) - (3 y z)}{y}$

Step 9

Factor $- 1$ out of $- 1 (2) - (3 y z)$ .

$- \frac{- 1 (2 + 3 y z)}{y}$

Step 10

Move the negative in front of the fraction.

$- - \frac{2 + 3 y z}{y}$

Step 11

Multiply $- 1$ by $- 1$ .

$1 \frac{2 + 3 y z}{y}$

Step 12

Multiply $\frac{2 + 3 y z}{y}$ by $1$ .

$\frac{2 + 3 y z}{y}$

Step 13

Split the fraction $\frac{2 + 3 y z}{y}$ into two fractions.

$\frac{2}{y} + \frac{3 y z}{y}$

Step 14

Cancel the common factor of $y$ .

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Step 14.1

Cancel the common factor.

$\frac{2}{y} + \frac{3 y z}{y}$

Step 14.2

Divide $3 z$ by $1$ .

$\frac{2}{y} + 3 z$