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

Sure! Let's go through each subtraction problem step by step and simplify the answers where possible. --- 1. **\(\frac{14}{9} - \frac{2}{9}\)** Both fractions have the same denominator, so subtract the numerators directly: \[ \frac{14}{9} - \frac{2}{9} = \frac{14 - 2}{9} = \frac{12}{9} \] Simplify by dividing numerator and denominator by 3: \[ \frac{12}{9} = \frac{4}{3} \] **Answer:** \(\frac{4}{3}\) --- 2. **\(\frac{2}{a - 1} - \frac{5}{a - 1}\)** Both fractions have the same denominator: \[ \frac{2}{a - 1} - \frac{5}{a - 1} = \frac{2 - 5}{a - 1} = \frac{-3}{a - 1} \] You can also write it as: \[ -\frac{3}{a - 1} \] **Answer:** \(-\frac{3}{a - 1}\) --- 3. **\(\frac{x + 4}{7} - \frac{x - 5}{7}\)** Same denominator allows direct subtraction: \[ \frac{x + 4}{7} - \frac{x - 5}{7} = \frac{(x + 4) - (x - 5)}{7} = \frac{x + 4 - x + 5}{7} = \frac{9}{7} \] **Answer:** \(\frac{9}{7}\) --- 4. **\(\frac{5}{2n} - \frac{2}{n}\)** First, find a common denominator, which is \(2n\): \[ \frac{5}{2n} - \frac{2}{n} = \frac{5}{2n} - \frac{4}{2n} = \frac{5 - 4}{2n} = \frac{1}{2n} \] **Answer:** \(\frac{1}{2n}\) --- 5. **\(\frac{3x}{2x + 1} - \frac{x}{2x + 1}\)** Same denominator allows direct subtraction: \[ \frac{3x}{2x + 1} - \frac{x}{2x + 1} = \frac{3x - x}{2x + 1} = \frac{2x}{2x + 1} \] **Answer:** \(\frac{2x}{2x + 1}\) --- 6. **\(\frac{x + 2}{x - 4} - \frac{3}{x + 1}\)** Different denominators require finding a common denominator, which is \((x - 4)(x + 1)\): \[ \frac{x + 2}{x - 4} = \frac{(x + 2)(x + 1)}{(x - 4)(x + 1)} = \frac{x^2 + 3x + 2}{(x - 4)(x + 1)} \] \[ \frac{3}{x + 1} = \frac{3(x - 4)}{(x - 4)(x + 1)} = \frac{3x - 12}{(x - 4)(x + 1)} \] Subtract the two fractions: \[ \frac{x^2 + 3x + 2}{(x - 4)(x + 1)} - \frac{3x - 12}{(x - 4)(x + 1)} = \frac{x^2 + 3x + 2 - 3x + 12}{(x - 4)(x + 1)} = \frac{x^2 + 14}{(x - 4)(x + 1)} \] **Answer:** \(\frac{x^2 + 14}{(x - 4)(x + 1)}\) --- 7. **\(\frac{x}{x}\)** Assuming \(x \neq 0\), the expression simplifies to: \[ \frac{x}{x} = 1 \] **Answer:** \(1\) (for \(x \neq 0\)) --- 8. **Additional Expressions** It seems there are a couple more expressions mentioned: - **\(x^2 - 9\):** \[ x^2 - 9 \] This is a difference of squares and can be factored as: \[ (x - 3)(x + 3) \] - **36:** If there's an equation or operation associated with 36, please provide more details for clarification. --- If you have any more problems or need further clarification on any of these steps, feel free to ask!