Divide (5x^4y^2+20xy^6-10x)/(5xy^2)

$\frac{(5 x^{4} y^{2} + 20 x y^{6} - 10 x)}{5 x y^{2}}$

Step 1

Factor $5 x$ out of $5 x^{4} y^{2} + 20 x y^{6} - 10 x$ .

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

$\frac{5 x (x^{3} y^{2}) + 20 x y^{6} - 10 x}{5 x y^{2}}$

Factor $5 x$ out of $20 x y^{6}$ .

$\frac{5 x (x^{3} y^{2}) + 5 x (4 y^{6}) - 10 x}{5 x y^{2}}$

Factor $5 x$ out of $- 10 x$ .

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

Factor $5 x$ out of $5 x (x^{3} y^{2}) + 5 x (4 y^{6})$ .

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

Factor $5 x$ out of $5 x (x^{3} y^{2} + 4 y^{6}) + 5 x (- 2)$ .

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

Step 2

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Split the fraction $\frac{x^{3} y^{2} + 4 y^{6} - 2}{y^{2}}$ into two fractions.

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

Step 5

Split the fraction $\frac{x^{3} y^{2} + 4 y^{6}}{y^{2}}$ into two fractions.

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

Step 6

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

Cancel the common factor.

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

Divide $x^{3}$ by $1$ .

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

Step 7

Cancel the common factor of $y^{6}$ and $y^{2}$ .

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $4 y^{4}$ by $1$ .

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

Step 8

Move the negative in front of the fraction.

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

Divide (5x^4y^2+20xy^6-10x)/(5xy^2)

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