Calculus Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $y$ .

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Step 2.1.1

Factor $y$ out of $x y$ .

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

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

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

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

Step 4

Cancel the common factor of $x + y$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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