Let $x$ be the number of prime numbers between 10 and 30 .

What is the number equal to $\frac{x^{2}-4}{x+2}$ ?

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The prime numbers between 10 and 30 are $11,13,17,19,23$, and 29 , which means $x=6$. Factoring the numerator in $\frac{x^{2}-4}{x+2}$ gives $\frac{(x-2)(x+2)}{x+2}$ which is equal to $x-2$ as long as $x \neq 2$.

Since $x=6$, the answer is $6-2=4$.