Algebra Examples

$\frac{- 6 x^{3} y - 9 x y + 18 x^{2} y^{2}}{3 x^{2} y}$

Step 1

Factor $3 x y$ out of $- 6 x^{3} y - 9 x y + 18 x^{2} y^{2}$ .

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Step 1.1

Factor $3 x y$ out of $- 6 x^{3} y$ .

$\frac{3 x y (- 2 x^{2}) - 9 x y + 18 x^{2} y^{2}}{3 x^{2} y}$

Step 1.2

Factor $3 x y$ out of $- 9 x y$ .

$\frac{3 x y (- 2 x^{2}) + 3 x y (- 3) + 18 x^{2} y^{2}}{3 x^{2} y}$

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $y$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Factor $- 1$ out of $- 2 x^{2}$ .

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

Step 6

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (2 x^{2}) - 1 (3) + 6 x y}{x}$

Step 7

Factor $- 1$ out of $- (2 x^{2}) - 1 (3)$ .

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

Step 8

Factor $- 1$ out of $6 x y$ .

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

Step 9

Factor $- 1$ out of $- (2 x^{2} + 3) - (- 6 x y)$ .

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

Step 10

Simplify the expression.

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Step 10.1

Rewrite $- (2 x^{2} + 3 - 6 x y)$ as $- 1 (2 x^{2} + 3 - 6 x y)$ .

$\frac{- 1 (2 x^{2} + 3 - 6 x y)}{x}$

Step 10.2

Move the negative in front of the fraction.

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