Solve for a3 a_3=(3^2-5)/(3^2+5)

$a_{3} = \frac{3^{2} - 5}{3^{2} + 5}$

Step 1

Simplify the numerator.

Raise $3$ to the power of $2$ .

$a_{3} = \frac{9 - 5}{3^{2} + 5}$

Subtract $5$ from $9$ .

$a_{3} = \frac{4}{3^{2} + 5}$

$a_{3} = \frac{4}{3^{2} + 5}$

Step 2

Simplify the denominator.

Raise $3$ to the power of $2$ .

$a_{3} = \frac{4}{9 + 5}$

Add $9$ and $5$ .

$a_{3} = \frac{4}{14}$

$a_{3} = \frac{4}{14}$

Step 3

Cancel the common factor of $4$ and $14$ .

Factor $2$ out of $4$ .

$a_{3} = \frac{2 (2)}{14}$

Cancel the common factors.

Factor $2$ out of $14$ .

$a_{3} = \frac{2 \cdot 2}{2 \cdot 7}$

Cancel the common factor.

$a_{3} = \frac{2 \cdot 2}{2 \cdot 7}$

Rewrite the expression.

$a_{3} = \frac{2}{7}$

$a_{3} = \frac{2}{7}$

$a_{3} = \frac{2}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a_{3} = \frac{2}{7}$

Decimal Form:

$a_{3} = 0.\overline{285714}$

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