Question

\[\lim_{h \rightarrow 0} (6/a+h)-(6/a)/h\]

Answer 1

\[\begin{align*}\lim_{h\to0}\frac{\dfrac{6}{a+h}-\dfrac{6}{a}}{h}&=\lim_{h\to0}\frac{\dfrac{6a}{a(a+h)}-\dfrac{6(a+h)}{a(a+h)}}{h}\\\\
&=\lim_{h\to0}\frac{\dfrac{6a-6(a+h)}{a(a+h)}}{h}\\\\\\
&=\lim_{h\to0}\frac{\dfrac{6a-6a-6h}{a(a+h)}}{h}\\\\\\
&=\lim_{h\to0}\frac{\dfrac{-6h}{a(a+h)}}{h}\\\\\\
&=\lim_{h\to0}\dfrac{-6}{a(a+h)}\\\\\\

\end{align*}\]