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- \documentclass[10pt]{article}
- \usepackage[a4paper,margin=1.5cm]{geometry}
- \usepackage{fouriernc}
- \usepackage{xcolor}
- \usepackage{amsmath}
- \usepackage[shortlabels]{enumitem}
- \begin{document}
- \begin{minipage}[t]{.475\textwidth}
- \textbf{Soal.}\\
- Bentuk sedrhana dari $\displaystyle\frac{\left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}{2\sqrt{5}-4\sqrt{2}}$ adalah \ldots.
- \begin{enumerate}[A.,leftmargin=*]
- \item $\displaystyle\tfrac{2}{3}\left(\sqrt{5}+2\sqrt{2}\right)$
- \item $\displaystyle\tfrac{2}{3}\left(2\sqrt{2}-\sqrt{5}\right)$
- \item $\displaystyle-\tfrac{2}{3}\left(2\sqrt{5}+4\sqrt{2}\right)$
- \item $\displaystyle-\tfrac{4}{9}\left(2\sqrt{5}+4\sqrt{2}\right)$
- \item $\displaystyle-\tfrac{4}{9}\left(2\sqrt{5}-\sqrt{2}\right)$
- \end{enumerate}
- \end{minipage}\hfill
- {\color{orange}\vrule}\hfill%
- \begin{minipage}[t]{.475\textwidth}
- \textbf{Jawaban: A}
- \begin{align*}
- \frac{\left(\sqrt{3}+\sqrt{7}\right)\left(\sqrt{3}-\sqrt{7}\right)}{2\sqrt{5}-4\sqrt{2}} &=
- \frac{3-7}{2\left(\sqrt{5}-2\sqrt{2}\right)} \\
- &= \frac{-4}{2\left(\sqrt{5}-2\sqrt{2}\right)}\\
- &= \frac{-2}{\sqrt{5}-2\sqrt{2}}{\color{red}{}\times\frac{\sqrt{5}+2\sqrt{2}}{\sqrt{5}+2\sqrt{2}}}\\
- &= \frac{-2\left(\sqrt{5}+2\sqrt{2}\right)}{5-8}\\
- &= \tfrac{2}{3}\left(\sqrt{5}+2\sqrt{2}\right)
- \end{align*}
- \end{minipage}
- \end{document}
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