a. \( \frac{9 x^{2}-12 x+4}{3 x^{2}-2 x} \) b. \( \frac{-9 x+6}{-18 x^{2}+12 x} \) c. \( \frac{9 x^{2}-4}{-3 x^{2}-11 x-6} \) d. \( \frac{21 x^{3}+14 x^{2}}{9 x^{2}+12 x+4} \) e. \( \frac{3 x^{2}+18 x+27}{3 x^{3}+16 x^{2}+15 x-18} \)

When simplifying rational expressions like these, remember that factoring is your best friend! Start by factoring both the numerator and denominator if possible, then look for common factors to cancel out. This can make the expression easier to work with and often reveals hidden solutions. Another key point is to watch out for common mistakes like ignoring restrictions on the variable. For instance, if you have a denominator that can equal zero for certain values of \(x\), those need to be excluded from your final answer. Not doing so can lead to incorrect conclusions or undefined expressions!