Algebra Examples

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

Step 1

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

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Step 1.1

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

$\frac{x^{3} y^{2} (1) + x^{4} y^{2} + x^{5} y^{2}}{x^{6} y}$

Step 1.2

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

$\frac{x^{3} y^{2} (1) + x^{3} y^{2} (x) + x^{5} y^{2}}{x^{6} y}$

Step 1.3

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

$\frac{x^{3} y^{2} (1) + x^{3} y^{2} (x) + x^{3} y^{2} (x^{2})}{x^{6} y}$

Step 1.4

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

$\frac{x^{3} y^{2} (1 + x) + x^{3} y^{2} (x^{2})}{x^{6} y}$

Step 1.5

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

$\frac{x^{3} y^{2} (1 + x + x^{2})}{x^{6} y}$

Step 2

Cancel the common factor of $x^{3}$ and $x^{6}$ .

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Step 2.1

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

$\frac{x^{3} (y^{2} (1 + x + x^{2}))}{x^{6} y}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

Factor $y$ out of $y^{2} (1 + x + x^{2})$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $y$ by $1$ .

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

Step 6

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

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

Step 7

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

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

Step 8

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

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Step 8.1

Factor $x$ out of $y x$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

$\frac{y}{x^{3}} + \frac{x y}{x \cdot x^{2}} + \frac{y x^{2}}{x^{3}}$

Step 8.2.2

Cancel the common factor.

$\frac{y}{x^{3}} + \frac{x y}{x \cdot x^{2}} + \frac{y x^{2}}{x^{3}}$

Step 8.2.3

Rewrite the expression.

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

Step 9

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

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Step 9.1

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

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

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

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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