Algebra Examples

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

Step 1

Factor $a$ out of $a x + a y$ .

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Step 1.1

Factor $a$ out of $a x$ .

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

Step 1.2

Factor $a$ out of $a y$ .

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

Step 1.3

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

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

Step 2

Factor $3$ out of $3 x + 3 y$ .

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Step 2.1

Factor $3$ out of $3 x$ .

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

Step 2.2

Factor $3$ out of $3 y$ .

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

Step 2.3

Factor $3$ out of $3 (x) + 3 (y)$ .

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

Step 3

Combine.

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

Step 4

Cancel the common factor of $x + y$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x$ out of $x y^{2} \cdot (3)$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y$ out of $y^{2} \cdot (3)$ .

$\frac{y (a (x))}{y (y \cdot 3)}$

Step 6.2.2

Cancel the common factor.

$\frac{y (a (x))}{y (y \cdot 3)}$

Step 6.2.3

Rewrite the expression.

$\frac{a (x)}{y \cdot 3}$

Step 7

Move $3$ to the left of $y$ .

$\frac{a x}{3 y}$