Divide (33x^5y^3+12x^4y^4-27x^3y^5-3x^2y^6)/(3x^3y^4)

$\frac{33 x^{5} y^{3} + 12 x^{4} y^{4} - 27 x^{3} y^{5} - 3 x^{2} y^{6}}{3 x^{3} y^{4}}$

Step 1

Simplify the numerator.

Factor $3 x^{2} y^{3}$ out of $33 x^{5} y^{3} + 12 x^{4} y^{4} - 27 x^{3} y^{5} - 3 x^{2} y^{6}$ .

Factor $3 x^{2} y^{3}$ out of $33 x^{5} y^{3}$ .

$\frac{3 x^{2} y^{3} (11 x^{3}) + 12 x^{4} y^{4} - 27 x^{3} y^{5} - 3 x^{2} y^{6}}{3 x^{3} y^{4}}$

Factor $3 x^{2} y^{3}$ out of $12 x^{4} y^{4}$ .

$\frac{3 x^{2} y^{3} (11 x^{3}) + 3 x^{2} y^{3} (4 x^{2} y) - 27 x^{3} y^{5} - 3 x^{2} y^{6}}{3 x^{3} y^{4}}$

Factor $3 x^{2} y^{3}$ out of $- 27 x^{3} y^{5}$ .

$\frac{3 x^{2} y^{3} (11 x^{3}) + 3 x^{2} y^{3} (4 x^{2} y) + 3 x^{2} y^{3} (- 9 x y^{2}) - 3 x^{2} y^{6}}{3 x^{3} y^{4}}$

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

$\frac{3 x^{2} y^{3} (11 x^{3}) + 3 x^{2} y^{3} (4 x^{2} y) + 3 x^{2} y^{3} (- 9 x y^{2}) + 3 x^{2} y^{3} (- 1 y^{3})}{3 x^{3} y^{4}}$

Factor $3 x^{2} y^{3}$ out of $3 x^{2} y^{3} (11 x^{3}) + 3 x^{2} y^{3} (4 x^{2} y)$ .

$\frac{3 x^{2} y^{3} (11 x^{3} + 4 x^{2} y) + 3 x^{2} y^{3} (- 9 x y^{2}) + 3 x^{2} y^{3} (- 1 y^{3})}{3 x^{3} y^{4}}$

Factor $3 x^{2} y^{3}$ out of $3 x^{2} y^{3} (11 x^{3} + 4 x^{2} y) + 3 x^{2} y^{3} (- 9 x y^{2})$ .

$\frac{3 x^{2} y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2}) + 3 x^{2} y^{3} (- 1 y^{3})}{3 x^{3} y^{4}}$

Factor $3 x^{2} y^{3}$ out of $3 x^{2} y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2}) + 3 x^{2} y^{3} (- 1 y^{3})$ .

$\frac{3 x^{2} y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - 1 y^{3})}{3 x^{3} y^{4}}$

Rewrite $- 1 y^{3}$ as $- y^{3}$ .

$\frac{3 x^{2} y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3})}{3 x^{3} y^{4}}$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2} y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3})}{3 x^{3} y^{4}}$

Rewrite the expression.

$\frac{x^{2} y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3})}{x^{3} y^{4}}$

Step 3

Cancel the common factor of $x^{2}$ and $x^{3}$ .

Factor $x^{2}$ out of $x^{2} y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3})$ .

$\frac{x^{2} (y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3}))}{x^{3} y^{4}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{3} y^{4}$ .

$\frac{x^{2} (y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3}))}{x^{2} (x y^{4})}$

Cancel the common factor.

$\frac{x^{2} (y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3}))}{x^{2} (x y^{4})}$

Rewrite the expression.

$\frac{y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3})}{x y^{4}}$

Step 4

Cancel the common factors.

Factor $y^{3}$ out of $x y^{4}$ .

$\frac{y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3})}{y^{3} (x y)}$

Cancel the common factor.

$\frac{y^{3} (11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3})}{y^{3} (x y)}$

Rewrite the expression.

$\frac{11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3}}{x y}$

Step 5

Split the fraction $\frac{11 x^{3} + 4 x^{2} y - 9 x y^{2} - y^{3}}{x y}$ into two fractions.

$\frac{11 x^{3} + 4 x^{2} y - 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Step 6

Split the fraction $\frac{11 x^{3} + 4 x^{2} y - 9 x y^{2}}{x y}$ into two fractions.

$\frac{11 x^{3} + 4 x^{2} y}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Step 7

Split the fraction $\frac{11 x^{3} + 4 x^{2} y}{x y}$ into two fractions.

$\frac{11 x^{3}}{x y} + \frac{4 x^{2} y}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Step 8

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $11 x^{3}$ .

$\frac{x (11 x^{2})}{x y} + \frac{4 x^{2} y}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Cancel the common factors.

Factor $x$ out of $x y$ .

$\frac{x (11 x^{2})}{x (y)} + \frac{4 x^{2} y}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Cancel the common factor.

$\frac{x (11 x^{2})}{x y} + \frac{4 x^{2} y}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Rewrite the expression.

$\frac{11 x^{2}}{y} + \frac{4 x^{2} y}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Step 9

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

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

$\frac{11 x^{2}}{y} + \frac{x (4 x y)}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Cancel the common factors.

Factor $x$ out of $x y$ .

$\frac{11 x^{2}}{y} + \frac{x (4 x y)}{x (y)} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Cancel the common factor.

$\frac{11 x^{2}}{y} + \frac{x (4 x y)}{x y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Rewrite the expression.

$\frac{11 x^{2}}{y} + \frac{4 x y}{y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Step 10

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{11 x^{2}}{y} + \frac{4 x y}{y} + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Divide $4 x$ by $1$ .

$\frac{11 x^{2}}{y} + 4 x + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Step 11

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{11 x^{2}}{y} + 4 x + \frac{- 9 x y^{2}}{x y} + \frac{- y^{3}}{x y}$

Rewrite the expression.

$\frac{11 x^{2}}{y} + 4 x + \frac{- 9 y^{2}}{y} + \frac{- y^{3}}{x y}$

Step 12

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

Factor $y$ out of $- 9 y^{2}$ .

$\frac{11 x^{2}}{y} + 4 x + \frac{y (- 9 y)}{y} + \frac{- y^{3}}{x y}$

Cancel the common factors.

Raise $y$ to the power of $1$ .

$\frac{11 x^{2}}{y} + 4 x + \frac{y (- 9 y)}{y^{1}} + \frac{- y^{3}}{x y}$

Factor $y$ out of $y^{1}$ .

$\frac{11 x^{2}}{y} + 4 x + \frac{y (- 9 y)}{y \cdot 1} + \frac{- y^{3}}{x y}$

Cancel the common factor.

$\frac{11 x^{2}}{y} + 4 x + \frac{y (- 9 y)}{y \cdot 1} + \frac{- y^{3}}{x y}$

Rewrite the expression.

$\frac{11 x^{2}}{y} + 4 x + \frac{- 9 y}{1} + \frac{- y^{3}}{x y}$

Divide $- 9 y$ by $1$ .

$\frac{11 x^{2}}{y} + 4 x - 9 y + \frac{- y^{3}}{x y}$

Step 13

Cancel the common factor of $y^{3}$ and $y$ .

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

$\frac{11 x^{2}}{y} + 4 x - 9 y + \frac{y (- y^{2})}{x y}$

Cancel the common factors.

Factor $y$ out of $x y$ .

$\frac{11 x^{2}}{y} + 4 x - 9 y + \frac{y (- y^{2})}{y x}$

Cancel the common factor.

$\frac{11 x^{2}}{y} + 4 x - 9 y + \frac{y (- y^{2})}{y x}$

Rewrite the expression.

$\frac{11 x^{2}}{y} + 4 x - 9 y + \frac{- y^{2}}{x}$

Step 14

Move the negative in front of the fraction.

$\frac{11 x^{2}}{y} + 4 x - 9 y - \frac{y^{2}}{x}$

Divide (33x^5y^3+12x^4y^4-27x^3y^5-3x^2y^6)/(3x^3y^4)

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