Divide (4x^2y+12x^2y^2-xy^2)/(4xy)

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

Step 1

Simplify the numerator.

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

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

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

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

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

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

$\frac{x y (4 x) + x y (12 x y) + x y (- 1 y)}{4 x y}$

Factor $x y$ out of $x y (4 x) + x y (12 x y)$ .

$\frac{x y (4 x + 12 x y) + x y (- 1 y)}{4 x y}$

Factor $x y$ out of $x y (4 x + 12 x y) + x y (- 1 y)$ .

$\frac{x y (4 x + 12 x y - 1 y)}{4 x y}$

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

$\frac{x y (4 x + 12 x y - y)}{4 x y}$

Step 2

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x y (4 x + 12 x y - y)}{4 x y}$

Rewrite the expression.

$\frac{y (4 x + 12 x y - y)}{4 y}$

Step 3

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{y (4 x + 12 x y - y)}{4 y}$

Rewrite the expression.

$\frac{4 x + 12 x y - y}{4}$

Step 4

Split the fraction $\frac{4 x + 12 x y - y}{4}$ into two fractions.

$\frac{4 x + 12 x y}{4} + \frac{- y}{4}$

Step 5

Split the fraction $\frac{4 x + 12 x y}{4}$ into two fractions.

$\frac{4 x}{4} + \frac{12 x y}{4} + \frac{- y}{4}$

Step 6

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} + \frac{12 x y}{4} + \frac{- y}{4}$

Divide $x$ by $1$ .

$x + \frac{12 x y}{4} + \frac{- y}{4}$

Step 7

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12 x y$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

$x + \frac{4 (3 x y)}{4 (1)} + \frac{- y}{4}$

Cancel the common factor.

$x + \frac{4 (3 x y)}{4 \cdot 1} + \frac{- y}{4}$

Rewrite the expression.

$x + \frac{3 x y}{1} + \frac{- y}{4}$

Divide $3 x y$ by $1$ .

$x + 3 x y + \frac{- y}{4}$

Step 8

Move the negative in front of the fraction.

$x + 3 x y - \frac{y}{4}$

Divide (4x^2y+12x^2y^2-xy^2)/(4xy)

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