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

Question

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

UpStudy AI · Accepted Answer

Sure! Let's go through each subtraction problem step by step and simplify the answers where possible.

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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:** $$\frac{4}{3}$$

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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:** $$-\frac{3}{a - 1}$$

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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:** $$\frac{9}{7}$$

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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:** $$\frac{1}{2n}$$

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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:** $$\frac{2x}{2x + 1}$$

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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:** $$\frac{x^2 + 14}{(x - 4)(x + 1)}$$

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7. **$$\frac{x}{x}$$**

Assuming $$x \neq 0$$, the expression simplifies to:
   $$
   \frac{x}{x} = 1
   $$

**Answer:** $$1$$ (for $$x \neq 0$$)

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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.

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If you have any more problems or need further clarification on any of these steps, feel free to ask!
$$ \begin{array}{l} \frac{14}{9} - \frac{2}{9} = \frac{4}{3} \ \frac{2}{a - 1} - \frac{5}{a - 1} = -\frac{3}{a - 1} \ \frac{x + 4}{7} - \frac{x - 5}{7} = \frac{9}{7} \ \frac{5}{2n} - \frac{2}{n} = \frac{1}{2n} \ \frac{3x}{2x + 1} - \frac{x}{2x + 1} = \frac{2x}{2x + 1} \ \frac{x + 2}{x - 4} - \frac{3}{x + 1} = \frac{x^2 + 14}{(x - 4)(x + 1)} \ \frac{x}{x} = 1 \quad (\text{for } x \neq 0) \ x^2 - 9 = (x - 3)(x + 3) \ 36 = 36 \end{array} $$

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