### Instruction: If $\frac{\sqrt{x}}{\sqrt{x-1}}=\frac32$, solve for $x$. Express your answer in simplest fractional form.### Response: I notice that the equation has a square root in the numerator and the denominator, so I want to get rid of them by squaring both sides.
Squaring both sides gives me $\frac{x}{x-1}=\frac94$.
Now I want to cross-multiply and simplify the equation.
I get $4x=9x-9$, which simplifies to $5x=9$.