Question

(\frac{n^{2}-4}{2}=16)

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation $\frac{n^2 - 4}{2}=16$ by 2 to get rid of the denominator.
$$2\times\frac{n^2 - 4}{2}=16\times2$$
Simplify both sides, we have $n^2 - 4 = 32$.

Step2: Solve for \(n^2\)

Add 4 to both sides of the equation $n^2 - 4 = 32$.
$$n^2 - 4 + 4 = 32 + 4$$
Simplify to get $n^2 = 36$.

Step3: Find the value of \(n\)

Take the square root of both sides of the equation $n^2 = 36$.
$$n=\pm\sqrt{36}$$
Since $\sqrt{36} = 6$, we get $n = 6$ or $n = - 6$.

Answer:

\(n = 6\) or \(n = - 6\)