Find and simplify the difference quotient for $f(x)=-\frac{7}{x}$. Be sure to completely simplify for full credit.
\[
\frac{f(x+h)-f(x)}{h}=\square \text { help (numbers) }
\]

Answer

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Answer

$\frac{f(x+h)-f(x)}{h} = \frac{\frac{7h}{x(x+h)}}{h} = \boxed{\frac{7}{x(x+h)}}$

Steps

Step 1 ：$f(x+h) = -\frac{7}{x+h}$

Step 2 ：$f(x+h)-f(x) = -\frac{7}{x+h} + \frac{7}{x}$

Step 3 ：$-\frac{7}{x+h} + \frac{7}{x} = \frac{-7x + 7(x+h)}{x(x+h)} = \frac{7h}{x(x+h)}$

Step 4 ：$\frac{f(x+h)-f(x)}{h} = \frac{\frac{7h}{x(x+h)}}{h} = \boxed{\frac{7}{x(x+h)}}$