Algebra Examples

$\frac{x^{2} - x y}{9 y^{2}} \div \frac{2 x}{3 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - x y}{9 y^{2}} \cdot \frac{3 y}{2 x}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $3 y$ .

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Step 2.1.1

Factor $3 y$ out of $9 y^{2}$ .

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

Multiply $\frac{x^{2} - x y}{3 y}$ by $\frac{1}{2 x}$ .

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

Step 2.3

Multiply $2$ by $3$ .

$\frac{x^{2} - x y}{6 y x}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

$\frac{x \cdot x - x y}{6 y x}$

Step 3.1.2

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

$\frac{x \cdot x + x (- 1 y)}{6 y x}$

Step 3.1.3

Factor $x$ out of $x \cdot x + x (- 1 y)$ .

$\frac{x (x - 1 y)}{6 y x}$

Step 3.2

Rewrite $- 1 y$ as $- y$ .

$\frac{x (x - y)}{6 y x}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

$\frac{x (x - y)}{6 y x}$

Step 4.2

Rewrite the expression.

$\frac{x - y}{6 y}$