I forgot how to do the algebra in this one.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\begin{array}{l}

f(x) = \frac{{ - 1}}{x};\,\,a = 1 \\

\\

f'(a) = \mathop {\lim }\limits_{h \to 0} \frac{{f(a + h) - f(a)}}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{\frac{{ - 1}}{{a + h}} - \frac{{ - 1}}{a}}}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{\frac{{ - 1a}}{{a(a + h)}} - \frac{{ - 1(a + h)}}{{a(a + h)}}}}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{\left( {\frac{{ - a - a + h}}{{a(a + h)}}} \right)}}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{\left( {\frac{{ - 2a + h}}{{a^2 + ah}}} \right)}}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{ - 2a + h}}{{a^2 + ah}}\,\,\frac{1}{h} = \\

\\

\mathop {\lim }\limits_{h \to 0} \frac{{ - 2a + h}}{{h\left( {a^2 + ah} \right)}} \\

\end{array}

[/tex]

Am I even going in the right direction? If so, what comes next?

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# Limit question / algebra problem

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