2. \( \frac{4 x^{2}-4}{4 x^{2}-6 x} \)

To simplify the expression \( \frac{4 x^{2}-4}{4 x^{2}-6 x} \), we start by factoring both the numerator and the denominator. The numerator can be factored as \( 4(x^{2} - 1) = 4(x - 1)(x + 1) \). For the denominator, we can factor out a common term, giving us \( 4x(x - \frac{3}{2}) \). Now our expression looks like this: \( \frac{4(x - 1)(x + 1)}{4x(x - \frac{3}{2})} \). The \( 4 \) in the numerator and denominator cancels out, simplifying to: \[ \frac{(x - 1)(x + 1)}{x(x - \frac{3}{2})} \] This is the simplified form of the fraction! To ensure we’re not missing anything important, let’s remember to check for any restrictions. Specifically, \( x \) cannot be \( 0 \) or \( \frac{3}{2} \) to avoid division by zero.