Divide (2x^3y^5z^6+8x^3y^5-12xy)/(4x^5y^3z)

$\frac{2 x^{3} y^{5} z^{6} + 8 x^{3} y^{5} - 12 x y}{4 x^{5} y^{3} z}$

Step 1

Factor $2 x y$ out of $2 x^{3} y^{5} z^{6} + 8 x^{3} y^{5} - 12 x y$ .

Factor $2 x y$ out of $2 x^{3} y^{5} z^{6}$ .

$\frac{2 x y (x^{2} y^{4} z^{6}) + 8 x^{3} y^{5} - 12 x y}{4 x^{5} y^{3} z}$

Factor $2 x y$ out of $8 x^{3} y^{5}$ .

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

Factor $2 x y$ out of $- 12 x y$ .

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

Factor $2 x y$ out of $2 x y (x^{2} y^{4} z^{6}) + 2 x y (4 x^{2} y^{4})$ .

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

Factor $2 x y$ out of $2 x y (x^{2} y^{4} z^{6} + 4 x^{2} y^{4}) + 2 x y (- 6)$ .

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

Step 2

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x y (x^{2} y^{4} z^{6} + 4 x^{2} y^{4} - 6)$ .

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

Cancel the common factors.

Factor $2$ out of $4 x^{5} y^{3} z$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ and $x^{5}$ .

Factor $x$ out of $x y (x^{2} y^{4} z^{6} + 4 x^{2} y^{4} - 6)$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Split the fraction $\frac{x^{2} y^{4} z^{6} + 4 x^{2} y^{4} - 6}{2 x^{4} y^{2} z}$ into two fractions.

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

Step 6

Split the fraction $\frac{x^{2} y^{4} z^{6} + 4 x^{2} y^{4}}{2 x^{4} y^{2} z}$ into two fractions.

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

Step 7

Cancel the common factor of $x^{2}$ and $x^{4}$ .

Factor $x^{2}$ out of $x^{2} y^{4} z^{6}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 8

Cancel the common factor of $y^{4}$ and $y^{2}$ .

Factor $y^{2}$ out of $y^{4} z^{6}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 9

Cancel the common factor of $z^{6}$ and $z$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{4 x^{2} y^{4}}{2 x^{4} y^{2} z} + \frac{- 6}{2 x^{4} y^{2} z}$

Step 10

Cancel the common factor of $4$ and $2$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 x^{2} y^{4}}{x^{4} y^{2} z} + \frac{- 6}{2 x^{4} y^{2} z}$

Step 11

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 y^{4}}{x^{2} y^{2} z} + \frac{- 6}{2 x^{4} y^{2} z}$

Step 12

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 y^{2}}{x^{2} z} + \frac{- 6}{2 x^{4} y^{2} z}$

Step 13

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

Factor $2$ out of $- 6$ .

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 y^{2}}{x^{2} z} + \frac{2 \cdot - 3}{2 x^{4} y^{2} z}$

Cancel the common factors.

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

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 y^{2}}{x^{2} z} + \frac{2 \cdot - 3}{2 (x^{4} y^{2} z)}$

Cancel the common factor.

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 y^{2}}{x^{2} z} + \frac{2 \cdot - 3}{2 (x^{4} y^{2} z)}$

Rewrite the expression.

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 y^{2}}{x^{2} z} + \frac{- 3}{x^{4} y^{2} z}$

Step 14

Move the negative in front of the fraction.

$\frac{y^{2} z^{5}}{2 x^{2}} + \frac{2 y^{2}}{x^{2} z} - \frac{3}{x^{4} y^{2} z}$

Divide (2x^3y^5z^6+8x^3y^5-12xy)/(4x^5y^3z)

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