<s>[INST] How to reduce this to have only one x ... Let $f(x)=\frac{5}{x+4} $
Reduce the difference quotient in the alternate definition of the derivative below so that you only have one x:
$$\frac{f(x) - f(2)}{x-2}$$
I've gotten down to $\frac{5(10-x)}{x-2}$ . but I can't figure out how to reduce it to one $x$. Am I doing something wrong? I have tried long division, which ended up being incorrect, so I have no idea.
 [/INST] Multiply up and down by $x + 4$
$$\frac{f(x) - f(2)}{x-2}=\frac{5-\frac{5}{6}(x+4)}{(x-2)(x+4)}$$
Multiply up and down by $6$
$$\frac{30-5(x+4)}{6(x-2)(x+4)} = \frac{-5x +10}{6(x-2)(x+4)} = \frac{-5(x-2)}{6(x-2)(x+4)} = -\frac{5}{6}\frac{1}{x+4}$$
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