Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Factor $a$ out of $a (a - 2) + a (a + 2)$ .

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

Step 5.2

Add $a$ and $a$ .

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

Step 5.3

Add $- 2$ and $2$ .

$\frac{a (2 a + 0)}{(a + 2) (a - 2)}$

Step 5.4

Add $2 a$ and $0$ .

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

Step 5.5

Combine exponents.

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Step 5.5.1

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

$\frac{2 (a^{1} a)}{(a + 2) (a - 2)}$

Step 5.5.2

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

$\frac{2 (a^{1} a^{1})}{(a + 2) (a - 2)}$

Step 5.5.3

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

$\frac{2 a^{1 + 1}}{(a + 2) (a - 2)}$

Step 5.5.4

Add $1$ and $1$ .

$\frac{2 a^{2}}{(a + 2) (a - 2)}$