b. simplify: \( \frac{a^{2}}{a-3}-\frac{9 a-6 a}{3-a}+\begin{array}{r}\text { solution- } \\ =\frac{a^{2}}{a-3}-\frac{6 a-9}{a-3}\end{array} \)

Let's break it down! First, note that \( 3 - a = -(a - 3) \), which allows us to rewrite the second term: \( \frac{9a - 6a}{3 - a} = \frac{3a}{-(a - 3)} = -\frac{3a}{a - 3} \). Now, it becomes clear that both fractions can share the common denominator \( a - 3 \): So, combining the fractions gives us: \[ \frac{a^{2}}{a-3} + \frac{3a}{a-3} = \frac{a^{2} + 3a}{a-3} \] This can be simplified further: \[ \frac{a(a + 3)}{a - 3} \] And there you have your simplified expression! Keep practicing, and you’ll be whipping through these in no time!