Pre-Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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 $b = y$ .

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Cancel the common factor of $x + y$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Divide $x - y$ by $1$ .

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

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Factor $x$ out of $y x$ .

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

Step 3.2.3

Factor $x$ out of $x \cdot x + x y$ .

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

Step 3.3

Cancel the common factor of $x$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Divide $x + y$ by $1$ .

$(x - y) (x + y)$

Step 4

Expand $(x - y) (x + y)$ using the FOIL Method.

Tap for more steps...

Step 4.1

Apply the distributive property.

$x (x + y) - y (x + y)$

Step 4.2

Apply the distributive property.

$x \cdot x + x y - y (x + y)$

Step 4.3

Apply the distributive property.

$x \cdot x + x y - y x - y \cdot y$

Step 5

Simplify terms.

Tap for more steps...

Step 5.1

Combine the opposite terms in $x \cdot x + x y - y x - y \cdot y$ .

Tap for more steps...

Step 5.1.1

Reorder the factors in the terms $x y$ and $- y x$ .

$x \cdot x + x y - x y - y \cdot y$

Step 5.1.2

Subtract $x y$ from $x y$ .

$x \cdot x + 0 - y \cdot y$

Step 5.1.3

Add $x \cdot x$ and $0$ .

$x \cdot x - y \cdot y$

Step 5.2

Simplify each term.

Tap for more steps...

Step 5.2.1

Multiply $x$ by $x$ .

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

Step 5.2.2

Multiply $y$ by $y$ by adding the exponents.

Tap for more steps...

Step 5.2.2.1

Move $y$ .

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

Step 5.2.2.2

Multiply $y$ by $y$ .

$x^{2} - y^{2}$