### Instruction: Find the value of $x$ that satisfies $\frac{\sqrt{5x}}{\sqrt{3(x-1)}}=2$. Express your answer in simplest fractional form.### Response: To solve for $x$, I want to isolate it on one side of the equation by using inverse operations.
First, I can multiply both sides by the denominator $\sqrt{3(x-1)}$ to clear the fraction.
This gives me $\sqrt{5x} = 2\sqrt{3(x-1)}$.
Next, I can square both sides to get rid of the square roots.
This gives me $5x = 4(3)(x-1)$.
Expanding the right-hand side, I get $5x = 12x - 12$.
Subtracting $12x$ from both sides, I get $-7x = -12$.
Dividing both sides by $-7$, I get $x = \frac{12}{7}$.