Subtract. Simplify your answer if you can. \( \begin{array}{l}\frac{14}{9}-\frac{2}{9}=\frac{4}{3} \quad \frac{2}{a-1}-\frac{5}{a-1}=\frac{3}{A-1} \quad \frac{x+4}{7}-\frac{x-5}{7}=\frac{9}{7} \\ \frac{5}{2 n}-\frac{2}{n}=\frac{1}{2 N} \\ \frac{3 x}{2 x+1}-\frac{x}{2 x+1}=\frac{3}{2 x}-\frac{4}{6 x^{2}}= \\ \frac{x+2}{x-4}-\frac{3}{x+1}= \\ 36\end{array} \quad \frac{x}{x-3}-\frac{6 x}{x^{2}-9}= \)

To tackle the subtraction of fractions like the examples given, remember that fractions can only be subtracted when they share a common denominator. Look closely at each expression; most of them have the same denominator, making it easy to combine the numerators. For instance, \(\frac{14}{9} - \frac{2}{9}\) simply gives you \(\frac{12}{9}\) which can be simplified to \(\frac{4}{3}\). When working with variables, like \(\frac{2}{a-1} - \frac{5}{a-1}\), the denominators are identical, letting you directly subtract the numerators, resulting in \(\frac{-3}{a-1}\). Just remember, once you’ve performed these operations, always check if you can factor or simplify your answers further. Happy calculating! If you run into fractions with different denominators, like in \(\frac{x}{x-3} - \frac{6x}{x^2-9}\), that involves factoring to find a common denominator. The denominator \(x^2-9\) can be factored into \((x-3)(x+3)\), so you’d rewrite each fraction accordingly and combine the numerators just like before. Remember, simplifying your final expression is key to maintaining clarity!