Pre-Algebra Examples

$\frac{20 x^{2} y^{3} - 10 y^{2} x^{2} - 7 y x + 2 y^{2}}{5 y^{2} x}$

Step 1

Factor $y$ out of $20 x^{2} y^{3} - 10 y^{2} x^{2} - 7 y x + 2 y^{2}$ .

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Step 1.1

Factor $y$ out of $20 x^{2} y^{3}$ .

$\frac{y (20 x^{2} y^{2}) - 10 y^{2} x^{2} - 7 y x + 2 y^{2}}{5 y^{2} x}$

Step 1.2

Factor $y$ out of $- 10 y^{2} x^{2}$ .

$\frac{y (20 x^{2} y^{2}) + y (- 10 y x^{2}) - 7 y x + 2 y^{2}}{5 y^{2} x}$

Step 1.3

Factor $y$ out of $- 7 y x$ .

$\frac{y (20 x^{2} y^{2}) + y (- 10 y x^{2}) + y (- 7 x) + 2 y^{2}}{5 y^{2} x}$

Step 1.4

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

$\frac{y (20 x^{2} y^{2}) + y (- 10 y x^{2}) + y (- 7 x) + y (2 y)}{5 y^{2} x}$

Step 1.5

Factor $y$ out of $y (20 x^{2} y^{2}) + y (- 10 y x^{2})$ .

$\frac{y (20 x^{2} y^{2} - 10 y x^{2}) + y (- 7 x) + y (2 y)}{5 y^{2} x}$

Step 1.6

Factor $y$ out of $y (20 x^{2} y^{2} - 10 y x^{2}) + y (- 7 x)$ .

$\frac{y (20 x^{2} y^{2} - 10 y x^{2} - 7 x) + y (2 y)}{5 y^{2} x}$

Step 1.7

Factor $y$ out of $y (20 x^{2} y^{2} - 10 y x^{2} - 7 x) + y (2 y)$ .

$\frac{y (20 x^{2} y^{2} - 10 y x^{2} - 7 x + 2 y)}{5 y^{2} x}$

Step 2

Cancel the common factors.

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Step 2.1

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

$\frac{y (20 x^{2} y^{2} - 10 y x^{2} - 7 x + 2 y)}{y (5 y x)}$

Step 2.2

Cancel the common factor.

$\frac{y (20 x^{2} y^{2} - 10 y x^{2} - 7 x + 2 y)}{y (5 y x)}$

Step 2.3

Rewrite the expression.

$\frac{20 x^{2} y^{2} - 10 y x^{2} - 7 x + 2 y}{5 y x}$

Step 3

Split the fraction $\frac{20 x^{2} y^{2} - 10 y x^{2} - 7 x + 2 y}{5 y x}$ into two fractions.

$\frac{20 x^{2} y^{2} - 10 y x^{2} - 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 4

Split the fraction $\frac{20 x^{2} y^{2} - 10 y x^{2} - 7 x}{5 y x}$ into two fractions.

$\frac{20 x^{2} y^{2} - 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 5

Split the fraction $\frac{20 x^{2} y^{2} - 10 y x^{2}}{5 y x}$ into two fractions.

$\frac{20 x^{2} y^{2}}{5 y x} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 6

Cancel the common factor of $20$ and $5$ .

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Step 6.1

Factor $5$ out of $20 x^{2} y^{2}$ .

$\frac{5 (4 x^{2} y^{2})}{5 y x} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $5 y x$ .

$\frac{5 (4 x^{2} y^{2})}{5 (y x)} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 6.2.2

Cancel the common factor.

$\frac{5 (4 x^{2} y^{2})}{5 (y x)} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 6.2.3

Rewrite the expression.

$\frac{4 x^{2} y^{2}}{y x} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 7

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

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Step 7.1

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

$\frac{x (4 x y^{2})}{y x} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x$ out of $y x$ .

$\frac{x (4 x y^{2})}{x y} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 7.2.2

Cancel the common factor.

$\frac{x (4 x y^{2})}{x y} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 7.2.3

Rewrite the expression.

$\frac{4 x y^{2}}{y} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 8

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

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Step 8.1

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

$\frac{y (4 x y)}{y} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

$\frac{y (4 x y)}{y^{1}} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 8.2.2

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

$\frac{y (4 x y)}{y \cdot 1} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 8.2.3

Cancel the common factor.

$\frac{y (4 x y)}{y \cdot 1} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 8.2.4

Rewrite the expression.

$\frac{4 x y}{1} + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 8.2.5

Divide $4 x y$ by $1$ .

$4 x y + \frac{- 10 y x^{2}}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 9

Cancel the common factor of $- 10$ and $5$ .

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Step 9.1

Factor $5$ out of $- 10 y x^{2}$ .

$4 x y + \frac{5 (- 2 y x^{2})}{5 y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $5$ out of $5 y x$ .

$4 x y + \frac{5 (- 2 y x^{2})}{5 (y x)} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 9.2.2

Cancel the common factor.

$4 x y + \frac{5 (- 2 y x^{2})}{5 (y x)} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 9.2.3

Rewrite the expression.

$4 x y + \frac{- 2 y x^{2}}{y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 10

Cancel the common factor of $y$ .

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Step 10.1

Cancel the common factor.

$4 x y + \frac{- 2 y x^{2}}{y x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 10.2

Rewrite the expression.

$4 x y + \frac{- 2 x^{2}}{x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 11

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

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Step 11.1

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

$4 x y + \frac{x (- 2 x)}{x} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

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

$4 x y + \frac{x (- 2 x)}{x^{1}} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 11.2.2

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

$4 x y + \frac{x (- 2 x)}{x \cdot 1} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 11.2.3

Cancel the common factor.

$4 x y + \frac{x (- 2 x)}{x \cdot 1} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 11.2.4

Rewrite the expression.

$4 x y + \frac{- 2 x}{1} + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 11.2.5

Divide $- 2 x$ by $1$ .

$4 x y - 2 x + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 12

Cancel the common factor of $x$ .

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Step 12.1

Cancel the common factor.

$4 x y - 2 x + \frac{- 7 x}{5 y x} + \frac{2 y}{5 y x}$

Step 12.2

Rewrite the expression.

$4 x y - 2 x + \frac{- 7}{5 y} + \frac{2 y}{5 y x}$

Step 13

Move the negative in front of the fraction.

$4 x y - 2 x - \frac{7}{5 y} + \frac{2 y}{5 y x}$

Step 14

Cancel the common factor of $y$ .

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Step 14.1

Cancel the common factor.

$4 x y - 2 x - \frac{7}{5 y} + \frac{2 y}{5 y x}$

Step 14.2

Rewrite the expression.

$4 x y - 2 x - \frac{7}{5 y} + \frac{2}{5 x}$