b. \( \frac{3 x}{5 x-15} \cdot \frac{x-3}{9 x^{2}} \)

Hey there, math enthusiast! Let's tackle this expression and simplify it step-by-step. First, factor out common terms where possible. Notice that the denominator \(5x - 15\) can be factored as \(5(x - 3)\). With this tidbit, the expression can be rewritten as: \[ \frac{3x}{5(x - 3)} \cdot \frac{x - 3}{9x^2} \] Now, you can see that \(x - 3\) cancels out! This simplifies the expression to: \[ \frac{3x}{5} \cdot \frac{1}{9x^2} = \frac{3}{45x} = \frac{1}{15x} \] And there you have it: the simplified form of the expression is \(\frac{1}{15x}\). Math magic at work! Now, before you rush off to celebrate your newfound mastery, remember: check for any restrictions! In this case, \(x\) cannot be 0 or 3, since that would make our original denominator undefined.