Pre-Algebra Examples

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

Step 1

To write $\frac{2 x}{x + 2}$ as a fraction with a common denominator, multiply by $\frac{x - 2}{x - 2}$ .

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

Step 2

To write $\frac{x + 2}{x - 2}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

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

Step 3

Write each expression with a common denominator of $(x + 2) (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Reorder the factors of $(x - 2) (x + 2)$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Apply the distributive property.

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

Step 5.2

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 5.2.1

Move $x$ .

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

Step 5.2.2

Multiply $x$ by $x$ .

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

Step 5.3

Multiply $- 2$ by $2$ .

$\frac{2 x^{2} - 4 x + (x + 2) (x + 2)}{(x + 2) (x - 2)}$

Step 5.4

Expand $(x + 2) (x + 2)$ using the FOIL Method.

Tap for more steps...

Step 5.4.1

Apply the distributive property.

$\frac{2 x^{2} - 4 x + x (x + 2) + 2 (x + 2)}{(x + 2) (x - 2)}$

Step 5.4.2

Apply the distributive property.

$\frac{2 x^{2} - 4 x + x \cdot x + x \cdot 2 + 2 (x + 2)}{(x + 2) (x - 2)}$

Step 5.4.3

Apply the distributive property.

$\frac{2 x^{2} - 4 x + x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2}{(x + 2) (x - 2)}$

Step 5.5

Simplify and combine like terms.

Tap for more steps...

Step 5.5.1

Simplify each term.

Tap for more steps...

Step 5.5.1.1

Multiply $x$ by $x$ .

$\frac{2 x^{2} - 4 x + x^{2} + x \cdot 2 + 2 x + 2 \cdot 2}{(x + 2) (x - 2)}$

Step 5.5.1.2

Move $2$ to the left of $x$ .

$\frac{2 x^{2} - 4 x + x^{2} + 2 \cdot x + 2 x + 2 \cdot 2}{(x + 2) (x - 2)}$

Step 5.5.1.3

Multiply $2$ by $2$ .

$\frac{2 x^{2} - 4 x + x^{2} + 2 x + 2 x + 4}{(x + 2) (x - 2)}$

Step 5.5.2

Add $2 x$ and $2 x$ .

$\frac{2 x^{2} - 4 x + x^{2} + 4 x + 4}{(x + 2) (x - 2)}$

Step 5.6

Add $2 x^{2}$ and $x^{2}$ .

$\frac{3 x^{2} - 4 x + 4 x + 4}{(x + 2) (x - 2)}$

Step 5.7

Add $- 4 x$ and $4 x$ .

$\frac{3 x^{2} + 0 + 4}{(x + 2) (x - 2)}$

Step 5.8

Add $3 x^{2}$ and $0$ .

$\frac{3 x^{2} + 4}{(x + 2) (x - 2)}$