Solve for a2 a_2=(2^2-2)/(2^2+2)

$a_{2} = \frac{2^{2} - 2}{2^{2} + 2}$

Step 1

Cancel the common factor of $2^{2} - 2$ and $2^{2} + 2$ .

Factor $- 1$ out of $2^{2}$ .

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

Rewrite $- 2$ as $- 1 (2)$ .

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

Factor $- 1$ out of $- 1 (- 2^{2}) - 1 (2)$ .

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

Factor $2$ out of $- 1 (- 2^{2} + 2)$ .

$a_{2} = \frac{2 (- 1 (- 1 \cdot 2 + 1))}{2^{2} + 2}$

Cancel the common factors.

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

$a_{2} = \frac{2 (- 1 (- 1 \cdot 2 + 1))}{2 \cdot 2 + 2}$

Factor $2$ out of $2$ .

$a_{2} = \frac{2 (- 1 (- 1 \cdot 2 + 1))}{2 \cdot 2 + 2 (1)}$

Factor $2$ out of $2 \cdot 2 + 2 (1)$ .

$a_{2} = \frac{2 (- 1 (- 1 \cdot 2 + 1))}{2 \cdot (2 + 1)}$

Cancel the common factor.

$a_{2} = \frac{2 (- 1 (- 1 \cdot 2 + 1))}{2 \cdot (2 + 1)}$

Rewrite the expression.

$a_{2} = \frac{- 1 (- 1 \cdot 2 + 1)}{2 + 1}$

Step 2

Simplify the numerator.

Multiply $- 1$ by $2$ .

$a_{2} = \frac{- 1 (- 2 + 1)}{2 + 1}$

Add $- 2$ and $1$ .

$a_{2} = \frac{- 1 \cdot - 1}{2 + 1}$

Step 3

Simplify the expression.

Add $2$ and $1$ .

$a_{2} = \frac{- 1 \cdot - 1}{3}$

Multiply $- 1$ by $- 1$ .

$a_{2} = \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a_{2} = \frac{1}{3}$

Decimal Form:

$a_{2} = 0.\overline{3}$