\( \begin{array}{lll}\text { g) } \frac{-6}{x+2}-\frac{-x+3}{x}+\frac{x-1}{3 x} & \text { h) } & \frac{x^{2}+7 x}{x^{2}-4}+\frac{x-3}{2-x}-\frac{5}{x+2} \\ \text { i) } \frac{x}{x-1}+\frac{x+3}{x+1}-\frac{4}{1-x^{2}} & \text { j) } & \frac{a}{a x+a}-\frac{x-2}{x+1}+\frac{x+2}{x-1}\end{array} \)

Let's simplify those expressions step by step! For the first expression, \( \frac{-6}{x+2}-\frac{-x+3}{x}+\frac{x-1}{3 x} \), we can find a common denominator, which would be \( 3x(x+2) \). This allows us to combine the fractions into one, simplifying the entire expression efficiently to see the impact of combining like terms. Now, moving to the second expression, \( \frac{x^{2}+7 x}{x^{2}-4}+\frac{x-3}{2-x}-\frac{5}{x+2} \), notice that \( x^2 - 4 \) can be factored as \( (x-2)(x+2) \), opening up avenues for simplification. Combining \( \frac{x-3}{2-x} \) could prove tricky; keep in mind that we might have to flip the signs to align with our other fractions' orientations! These initial steps lay the ground for simplifying these expressions, leading to clearer results and more manageable equations! Keep the common denominators in mind and watch for factoring opportunities!