Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.1.4

Factor $x y$ out of $x y (6 x) + x y (12 x y)$ .

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

Step 1.1.5

Factor $x y$ out of $x y (6 x + 12 x y) + x y (- 1 y)$ .

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

Step 1.2

Rewrite $- 1 y$ as $- y$ .

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

Step 2

Cancel the common factor of $x$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factor of $y$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{6 x + 12 x y - y}{6}$

Step 4

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

$\frac{6 x + 12 x y}{6} + \frac{- y}{6}$

Step 5

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

$\frac{6 x}{6} + \frac{12 x y}{6} + \frac{- y}{6}$

Step 6

Cancel the common factor of $6$ .

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Step 6.1

Cancel the common factor.

$\frac{6 x}{6} + \frac{12 x y}{6} + \frac{- y}{6}$

Step 6.2

Divide $x$ by $1$ .

$x + \frac{12 x y}{6} + \frac{- y}{6}$

Step 7

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

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Step 7.1

Factor $6$ out of $12 x y$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $6$ out of $6$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$x + \frac{2 x y}{1} + \frac{- y}{6}$

Step 7.2.4

Divide $2 x y$ by $1$ .

$x + 2 x y + \frac{- y}{6}$

Step 8

Move the negative in front of the fraction.

$x + 2 x y - \frac{y}{6}$