Pre-Algebra Examples

$\frac{x y}{x y + 1} \div \frac{x}{y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Cancel the common factor of $x$ .

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Step 2.1

Factor $x$ out of $x y$ .

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

Step 2.2

Cancel the common factor.

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

Step 2.3

Rewrite the expression.

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

Step 3

Combine $\frac{y}{x y + 1}$ and $y$ .

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

Add $1$ and $1$ .

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