Algebra Examples

$\frac{12 x^{2} y - 6 x y + 4 x^{2}}{2 x y}$

Step 1

Factor $2 x$ out of $12 x^{2} y - 6 x y + 4 x^{2}$ .

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Step 1.1

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

$\frac{2 x (6 x y) - 6 x y + 4 x^{2}}{2 x y}$

Step 1.2

Factor $2 x$ out of $- 6 x y$ .

$\frac{2 x (6 x y) + 2 x (- 3 y) + 4 x^{2}}{2 x y}$

Step 1.3

Factor $2 x$ out of $4 x^{2}$ .

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

Step 1.4

Factor $2 x$ out of $2 x (6 x y) + 2 x (- 3 y)$ .

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

Step 1.5

Factor $2 x$ out of $2 x (6 x y - 3 y) + 2 x (2 x)$ .

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Split the fraction $\frac{6 x y - 3 y + 2 x}{y}$ into two fractions.

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

Step 5

Split the fraction $\frac{6 x y - 3 y}{y}$ into two fractions.

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

Step 6

Cancel the common factor of $y$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Divide $6 x$ by $1$ .

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

Step 7

Cancel the common factor of $y$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Divide $- 3$ by $1$ .

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