Precalculus Examples

$\frac{12 x^{2} y^{3} - 18 x y^{2} + y^{2}}{- 6 x y}$

Step 1

Factor $y^{2}$ out of $12 x^{2} y^{3} - 18 x y^{2} + y^{2}$ .

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Step 1.1

Factor $y^{2}$ out of $12 x^{2} y^{3}$ .

$\frac{y^{2} (12 x^{2} y) - 18 x y^{2} + y^{2}}{- 6 x y}$

Step 1.2

Factor $y^{2}$ out of $- 18 x y^{2}$ .

$\frac{y^{2} (12 x^{2} y) + y^{2} (- 18 x) + y^{2}}{- 6 x y}$

Step 1.3

Multiply by $1$ .

$\frac{y^{2} (12 x^{2} y) + y^{2} (- 18 x) + y^{2} \cdot 1}{- 6 x y}$

Step 1.4

Factor $y^{2}$ out of $y^{2} (12 x^{2} y) + y^{2} (- 18 x)$ .

$\frac{y^{2} (12 x^{2} y - 18 x) + y^{2} \cdot 1}{- 6 x y}$

Step 1.5

Factor $y^{2}$ out of $y^{2} (12 x^{2} y - 18 x) + y^{2} \cdot 1$ .

$\frac{y^{2} (12 x^{2} y - 18 x + 1)}{- 6 x y}$

Step 2

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

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Step 2.1

Factor $y$ out of $y^{2} (12 x^{2} y - 18 x + 1)$ .

$\frac{y (y (12 x^{2} y - 18 x + 1))}{- 6 x y}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $y$ out of $- 6 x y$ .

$\frac{y (y (12 x^{2} y - 18 x + 1))}{y (- 6 x)}$

Step 2.2.2

Cancel the common factor.

$\frac{y (y (12 x^{2} y - 18 x + 1))}{y (- 6 x)}$

Step 2.2.3

Rewrite the expression.

$\frac{y (12 x^{2} y - 18 x + 1)}{- 6 x}$

Step 3

Move the negative in front of the fraction.

$- \frac{y (12 x^{2} y - 18 x + 1)}{6 x}$

Step 4

Apply the distributive property.

$- \frac{y (12 x^{2} y) + y (- 18 x) + y \cdot 1}{6 x}$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$- \frac{12 y (x^{2} y) + y (- 18 x) + y \cdot 1}{6 x}$

Step 5.2

Rewrite using the commutative property of multiplication.

$- \frac{12 y (x^{2} y) - 18 y x + y \cdot 1}{6 x}$

Step 5.3

Multiply $y$ by $1$ .

$- \frac{12 y (x^{2} y) - 18 y x + y}{6 x}$

Step 6

Multiply $y$ by $y$ by adding the exponents.

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Step 6.1

Move $y$ .

$- \frac{12 (y \cdot y) x^{2} - 18 y x + y}{6 x}$

Step 6.2

Multiply $y$ by $y$ .

$- \frac{12 y^{2} x^{2} - 18 y x + y}{6 x}$

Step 7

Split the fraction $\frac{12 y^{2} x^{2} - 18 y x + y}{6 x}$ into two fractions.

$- (\frac{12 y^{2} x^{2} - 18 y x}{6 x} + \frac{y}{6 x})$

Step 8

Split the fraction $\frac{12 y^{2} x^{2} - 18 y x}{6 x}$ into two fractions.

$- (\frac{12 y^{2} x^{2}}{6 x} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 9

Cancel the common factor of $12$ and $6$ .

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Step 9.1

Factor $6$ out of $12 y^{2} x^{2}$ .

$- (\frac{6 (2 y^{2} x^{2})}{6 x} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $6$ out of $6 x$ .

$- (\frac{6 (2 y^{2} x^{2})}{6 (x)} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 9.2.2

Cancel the common factor.

$- (\frac{6 (2 y^{2} x^{2})}{6 x} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 9.2.3

Rewrite the expression.

$- (\frac{2 y^{2} x^{2}}{x} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 10

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

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Step 10.1

Factor $x$ out of $2 y^{2} x^{2}$ .

$- (\frac{x (2 y^{2} x)}{x} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

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

$- (\frac{x (2 y^{2} x)}{x^{1}} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 10.2.2

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

$- (\frac{x (2 y^{2} x)}{x \cdot 1} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 10.2.3

Cancel the common factor.

$- (\frac{x (2 y^{2} x)}{x \cdot 1} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 10.2.4

Rewrite the expression.

$- (\frac{2 y^{2} x}{1} + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 10.2.5

Divide $2 y^{2} x$ by $1$ .

$- (2 y^{2} x + \frac{- 18 y x}{6 x} + \frac{y}{6 x})$

Step 11

Cancel the common factor of $- 18$ and $6$ .

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Step 11.1

Factor $6$ out of $- 18 y x$ .

$- (2 y^{2} x + \frac{6 (- 3 y x)}{6 x} + \frac{y}{6 x})$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $6$ out of $6 x$ .

$- (2 y^{2} x + \frac{6 (- 3 y x)}{6 (x)} + \frac{y}{6 x})$

Step 11.2.2

Cancel the common factor.

$- (2 y^{2} x + \frac{6 (- 3 y x)}{6 x} + \frac{y}{6 x})$

Step 11.2.3

Rewrite the expression.

$- (2 y^{2} x + \frac{- 3 y x}{x} + \frac{y}{6 x})$

Step 12

Cancel the common factor of $x$ .

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Step 12.1

Cancel the common factor.

$- (2 y^{2} x + \frac{- 3 y x}{x} + \frac{y}{6 x})$

Step 12.2

Divide $- 3 y$ by $1$ .

$- (2 y^{2} x - 3 y + \frac{y}{6 x})$