Divide (2x^2y+6x^2y^2-xy^2)/(2xy)

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

Step 1

Simplify the numerator.

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

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

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

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

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

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

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

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

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

Factor $x y$ out of $x y (2 x + 6 x y) + x y (- 1 y)$ .

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

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

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

Step 2

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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

Step 5

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

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

Step 6

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 7

Cancel the common factor of $6$ and $2$ .

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

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x + \frac{3 x y}{1} + \frac{- y}{2}$

Divide $3 x y$ by $1$ .

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

Step 8

Move the negative in front of the fraction.

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

Divide (2x^2y+6x^2y^2-xy^2)/(2xy)

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