Algebra Examples

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

Step 1

Factor $a^{2}$ out of $a^{2} + a^{3}$ .

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Step 1.1

Multiply by $1$ .

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

Step 1.2

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

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

Step 1.3

Factor $a^{2}$ out of $a^{2} \cdot 1 + a^{2} a$ .

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

Step 2

Factor $a$ out of $a + a^{2}$ .

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Factor $a$ out of $a \cdot 1 + a \cdot a$ .

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

Step 3

Combine.

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

Step 4

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

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Step 4.1

Factor $x$ out of $x y (a (1 + a))$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factors.

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

Cancel the common factors.

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Step 6.1

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

$\frac{a (1 + a)}{a ((a (1 + a)) (x y))}$

Step 6.2

Cancel the common factor.

$\frac{a (1 + a)}{a ((a (1 + a)) (x y))}$

Step 6.3

Rewrite the expression.

$\frac{1 + a}{(a (1 + a)) (x y)}$

Step 7

Cancel the common factor of $1 + a$ .

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Step 7.1

Cancel the common factor.

$\frac{1 + a}{a (1 + a) (x y)}$

Step 7.2

Rewrite the expression.

$\frac{1}{(a) (x y)}$

$\frac{1}{a x y}$