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

Calculate the value by following steps: - step0: Calculate: \(\frac{14}{9}-\frac{2}{9}\) - step1: Transform the expression: \(\frac{14-2}{9}\) - step2: Subtract the numbers: \(\frac{12}{9}\) - step3: Reduce the fraction: \(\frac{4}{3}\) Calculate or simplify the expression \( 5/(2*n) - 2/n \). Simplify the expression by following steps: - step0: Solution: \(\frac{5}{2n}-\frac{2}{n}\) - step1: Reduce fractions to a common denominator: \(\frac{5}{2n}-\frac{2\times 2}{n\times 2}\) - step2: Reorder the terms: \(\frac{5}{2n}-\frac{2\times 2}{2n}\) - step3: Transform the expression: \(\frac{5-2\times 2}{2n}\) - step4: Multiply the numbers: \(\frac{5-4}{2n}\) - step5: Subtract the numbers: \(\frac{1}{2n}\) Calculate or simplify the expression \( 2/(a-1) - 5/(a-1) \). Simplify the expression by following steps: - step0: Solution: \(\frac{2}{\left(a-1\right)}-\frac{5}{\left(a-1\right)}\) - step1: Remove the parentheses: \(\frac{2}{a-1}-\frac{5}{a-1}\) - step2: Transform the expression: \(\frac{2-5}{a-1}\) - step3: Subtract the numbers: \(\frac{-3}{a-1}\) - step4: Rewrite the fraction: \(-\frac{3}{a-1}\) Calculate or simplify the expression \( (x+4)/7 - (x-5)/7 \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(x+4\right)}{7}-\frac{\left(x-5\right)}{7}\) - step1: Remove the parentheses: \(\frac{x+4}{7}-\frac{x-5}{7}\) - step2: Transform the expression: \(\frac{x+4-\left(x-5\right)}{7}\) - step3: Calculate: \(\frac{9}{7}\) Calculate or simplify the expression \( (3*x)/(2*x+1) - x/(2*x+1) \). Simplify the expression by following steps: - step0: Solution: \(\frac{3x}{\left(2x+1\right)}-\frac{x}{\left(2x+1\right)}\) - step1: Remove the parentheses: \(\frac{3x}{2x+1}-\frac{x}{2x+1}\) - step2: Transform the expression: \(\frac{3x-x}{2x+1}\) - step3: Subtract the terms: \(\frac{2x}{2x+1}\) Calculate or simplify the expression \( x/(x-3) - 6*x/(x^2-9) \). Simplify the expression by following steps: - step0: Solution: \(\frac{x}{\left(x-3\right)}-\frac{6x}{\left(x^{2}-9\right)}\) - step1: Remove the parentheses: \(\frac{x}{x-3}-\frac{6x}{x^{2}-9}\) - step2: Factor the expression: \(\frac{x}{x-3}-\frac{6x}{\left(x+3\right)\left(x-3\right)}\) - step3: Reduce fractions to a common denominator: \(\frac{x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{6x}{\left(x+3\right)\left(x-3\right)}\) - step4: Rewrite the expression: \(\frac{x\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}-\frac{6x}{\left(x+3\right)\left(x-3\right)}\) - step5: Transform the expression: \(\frac{x\left(x+3\right)-6x}{\left(x+3\right)\left(x-3\right)}\) - step6: Multiply the terms: \(\frac{x^{2}+3x-6x}{\left(x+3\right)\left(x-3\right)}\) - step7: Subtract the terms: \(\frac{x^{2}-3x}{\left(x+3\right)\left(x-3\right)}\) - step8: Factor the expression: \(\frac{x\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}\) - step9: Reduce the fraction: \(\frac{x}{x+3}\) Calculate or simplify the expression \( (x+2)/(x-4) - 3/(x+1) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(x+2\right)}{\left(x-4\right)}-\frac{3}{\left(x+1\right)}\) - step1: Remove the parentheses: \(\frac{x+2}{x-4}-\frac{3}{x+1}\) - step2: Reduce fractions to a common denominator: \(\frac{\left(x+2\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}-\frac{3\left(x-4\right)}{\left(x+1\right)\left(x-4\right)}\) - step3: Rewrite the expression: \(\frac{\left(x+2\right)\left(x+1\right)}{\left(x-4\right)\left(x+1\right)}-\frac{3\left(x-4\right)}{\left(x-4\right)\left(x+1\right)}\) - step4: Transform the expression: \(\frac{\left(x+2\right)\left(x+1\right)-3\left(x-4\right)}{\left(x-4\right)\left(x+1\right)}\) - step5: Multiply the terms: \(\frac{x^{2}+3x+2-3\left(x-4\right)}{\left(x-4\right)\left(x+1\right)}\) - step6: Multiply the terms: \(\frac{x^{2}+3x+2-\left(3x-12\right)}{\left(x-4\right)\left(x+1\right)}\) - step7: Calculate: \(\frac{x^{2}+14}{\left(x-4\right)\left(x+1\right)}\) - step8: Multiply the terms: \(\frac{x^{2}+14}{x^{2}-3x-4}\) Let's go through each subtraction step by step and simplify the results where possible. 1. **First Expression:** \[ \frac{14}{9} - \frac{2}{9} = \frac{14 - 2}{9} = \frac{12}{9} = \frac{4}{3} \] 2. **Second Expression:** \[ \frac{2}{a-1} - \frac{5}{a-1} = \frac{2 - 5}{a-1} = \frac{-3}{a-1} \] 3. **Third Expression:** \[ \frac{x+4}{7} - \frac{x-5}{7} = \frac{(x+4) - (x-5)}{7} = \frac{x + 4 - x + 5}{7} = \frac{9}{7} \] 4. **Fourth Expression:** \[ \frac{5}{2n} - \frac{2}{n} = \frac{5}{2n} - \frac{4}{2n} = \frac{5 - 4}{2n} = \frac{1}{2n} \] 5. **Fifth Expression:** \[ \frac{3x}{2x+1} - \frac{x}{2x+1} = \frac{3x - x}{2x+1} = \frac{2x}{2x+1} \] 6. **Sixth Expression:** \[ \frac{x+2}{x-4} - \frac{3}{x+1} = \frac{(x+2)(x+1) - 3(x-4)}{(x-4)(x+1)} \] Expanding the numerator: \[ (x^2 + x + 2x + 2) - (3x - 12) = x^2 + 3x + 2 - 3x + 12 = x^2 + 14 \] Thus, we have: \[ \frac{x^2 + 14}{(x-4)(x+1)} \] 7. **Seventh Expression:** \[ \frac{x}{x-3} - \frac{6x}{x^2-9} = \frac{x}{x-3} - \frac{6x}{(x-3)(x+3)} = \frac{x(x+3) - 6x}{(x-3)(x+3)} = \frac{x^2 + 3x - 6x}{(x-3)(x+3)} = \frac{x^2 - 3x}{(x-3)(x+3)} \] This can be simplified to: \[ \frac{x(x-3)}{(x-3)(x+3)} = \frac{x}{x+3} \quad (x \neq 3) \] ### Summary of Results: 1. \( \frac{14}{9} - \frac{2}{9} = \frac{4}{3} \) 2. \( \frac{2}{a-1} - \frac{5}{a-1} = -\frac{3}{a-1} \) 3. \( \frac{x+4}{7} - \frac{x-5}{7} = \frac{9}{7} \) 4. \( \frac{5}{2n} - \frac{2}{n} = \frac{1}{2n} \) 5. \( \frac{3x}{2x+1} - \frac{x}{2x+1} = \frac{2x}{2x+1} \) 6. \( \frac{x+2}{x-4} - \frac{3}{x+1} = \frac{x^2 + 14}{(x-4)(x+1)} \) 7. \( \frac{x}{x-3} - \frac{6x}{x^2-9} = \frac{x}{x+3} \) (for \( x \neq 3 \))