We are given that $x \star 24 = 7$ and $a \star b = \frac{\sqrt{a+b}}{\sqrt{a-b}}$.
Substituting $x$ into the expression for $x \star 24$, we have $\frac{\sqrt{x+24}}{\sqrt{x-24}} = 7$.
Squaring both sides, we get $\frac{x+24}{x-24} = 49$.
Cross-multiplying, we have $x+24 = 49(x-24)$.
Expanding and simplifying, we have $x+24 = 49x - 1176$.
Collecting like terms, we have $48x = 1200$.
Dividing both sides by 48, we have $x = \boxed{25}$.
The answer is: 25
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If $x \star 24 = 7$ and $a \star b = \frac{\sqrt{a+b}}{\sqrt{a-b}}$, what is the value of $x$?

### Answer:
