Solve for a4 a_4=(4^2-12)/(4^2+12)

$a_{4} = \frac{4^{2} - 12}{4^{2} + 12}$

Step 1

Simplify the numerator.

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

$a_{4} = \frac{16 - 12}{4^{2} + 12}$

Subtract $12$ from $16$ .

$a_{4} = \frac{4}{4^{2} + 12}$

$a_{4} = \frac{4}{4^{2} + 12}$

Step 2

Simplify the denominator.

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

$a_{4} = \frac{4}{16 + 12}$

Add $16$ and $12$ .

$a_{4} = \frac{4}{28}$

$a_{4} = \frac{4}{28}$

Step 3

Cancel the common factor of $4$ and $28$ .

Factor $4$ out of $4$ .

$a_{4} = \frac{4 (1)}{28}$

Cancel the common factors.

Factor $4$ out of $28$ .

$a_{4} = \frac{4 \cdot 1}{4 \cdot 7}$

Cancel the common factor.

$a_{4} = \frac{4 \cdot 1}{4 \cdot 7}$

Rewrite the expression.

$a_{4} = \frac{1}{7}$

$a_{4} = \frac{1}{7}$

$a_{4} = \frac{1}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a_{4} = \frac{1}{7}$

Decimal Form:

$a_{4} = 0.\overline{142857}$

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