Solve for a4 a_4=(4^2-2)/(4^2+2)

$a_{4} = \frac{4^{2} - 2}{4^{2} + 2}$

Step 1

Simplify the numerator.

Raise $4$ to the power of $2$ .

$a_{4} = \frac{16 - 2}{4^{2} + 2}$

Subtract $2$ from $16$ .

$a_{4} = \frac{14}{4^{2} + 2}$

$a_{4} = \frac{14}{4^{2} + 2}$

Step 2

Simplify the denominator.

Raise $4$ to the power of $2$ .

$a_{4} = \frac{14}{16 + 2}$

Add $16$ and $2$ .

$a_{4} = \frac{14}{18}$

$a_{4} = \frac{14}{18}$

Step 3

Cancel the common factor of $14$ and $18$ .

Factor $2$ out of $14$ .

$a_{4} = \frac{2 (7)}{18}$

Cancel the common factors.

Factor $2$ out of $18$ .

$a_{4} = \frac{2 \cdot 7}{2 \cdot 9}$

Cancel the common factor.

$a_{4} = \frac{2 \cdot 7}{2 \cdot 9}$

Rewrite the expression.

$a_{4} = \frac{7}{9}$

$a_{4} = \frac{7}{9}$

$a_{4} = \frac{7}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a_{4} = \frac{7}{9}$

Decimal Form:

$a_{4} = 0.\overline{7}$

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