Find the difference quotient $$ \frac{f(x+h)-f(x)}{h} $$ of $$ f(x)=-\frac{8}{15 x+9} $$ (Use symbolic notation and fractions where needed.) 14$$ \rangle $$ $$ \frac{f(x+h)-f(x)}{h}=\square $$

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To find the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for the function $$ f(x) = -\frac{8}{15x + 9} $$, follow these steps:

1. **Compute $$ f(x+h) $$:**
   $$
   f(x+h) = -\frac{8}{15(x+h) + 9} = -\frac{8}{15x + 15h + 9}
   $$

2. **Compute the difference $$ f(x+h) - f(x) $$:**
   $$
   f(x+h) - f(x) = -\frac{8}{15x + 15h + 9} - \left(-\frac{8}{15x + 9}\right) = \frac{8}{15x + 9} - \frac{8}{15x + 15h + 9}
   $$

3. **Combine the fractions:**
   $$
   \frac{8}{15x + 9} - \frac{8}{15x + 15h + 9} = 8 \left( \frac{1}{15x + 9} - \frac{1}{15x + 15h + 9} \right)
   $$
   $$
   = 8 \cdot \frac{(15x + 15h + 9) - (15x + 9)}{(15x + 9)(15x + 15h + 9)}
   $$
   $$
   = 8 \cdot \frac{15h}{(15x + 9)(15x + 15h + 9)} = \frac{120h}{(15x + 9)(15x + 15h + 9)}
   $$

4. **Divide by $$ h $$ to get the difference quotient:**
   $$
   \frac{f(x+h) - f(x)}{h} = \frac{120h}{(15x + 9)(15x + 15h + 9)} \cdot \frac{1}{h} = \frac{120}{(15x + 9)(15x + 15h + 9)}
   $$

5. **Simplify if desired:**
   You can factor out common terms to simplify further:
   $$
   = \frac{40}{3(5x + 3)(5x + 5h + 3)}
   $$

However, the most straightforward form is:

$$
\frac{f(x+h)-f(x)}{h} = \frac{120}{(15x + 9)(15x + 15h + 9)}
$$

**Final Answer:**
$$
\frac{f(x+h)-f(x)}{h} = \frac{120}{\, (15x + 9)(15x + 15h + 9)\,}
$$
$$ \frac{f(x+h)-f(x)}{h} = \frac{120}{(15x + 9)(15x + 15h + 9)} $$

Find the difference quotient of

(Use symbolic notation and fractions where needed.) 14

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Find the difference quotient of (Use symbolic notation and fractions where needed.) 14