Algebra Examples

$\frac{x}{y} \div \frac{y}{x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Multiply $\frac{x}{y} \cdot \frac{x}{y}$ .

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Step 2.1

Multiply $\frac{x}{y}$ by $\frac{x}{y}$ .

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

Step 2.2

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

$\frac{x^{1} x}{y \cdot y}$

Step 2.3

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

$\frac{x^{1} x^{1}}{y \cdot y}$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.5

Add $1$ and $1$ .

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

Step 2.6

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

$\frac{x^{2}}{y^{1} y}$

Step 2.7

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

$\frac{x^{2}}{y^{1} y^{1}}$

Step 2.8

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.9

Add $1$ and $1$ .

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