\documentclass[12pt,twoside]{article}
\usepackage{amsmath,amssymb,graphicx}
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\newcommand{\coursenumber}{Math 042}
\newcommand{\coursetitle}{Intermediate Algebra}
\newcommand{\docdate}{April 26, 2010}
\newcommand{\duedate}{April 26, 2010}
\newcommand{\doctitle}{Exam III}
\newcommand{\student}{PUT YOUR NAME HERE}

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\begin{document}

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%\begin{center}
%\Large\bf\coursenumber\\[2pt]\doctitle \\ \large\docdate
%\end{center}

%\paragraph{}
%The point value of each problem is shown in [ ]. To receive full
%credit all your answers should be carefully justified.
%Each solution must be the student's own work. 

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\begin{center}\framebox{\parbox{\boxlength}{\bf
Math 042: Exam III \hfill Date: \docdate\\ ~\\~\\
Name: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$    \hfill Section: $\_\_\_\_\_\_\_\_\_\_\_\_\_$}}
\end{center}

%\problembreak
\noindent
\paragraph{1.} Perform the indicated operation and simplify.
\[
\frac{1}{k+3} + \frac{4}{3k}
\]

\ni
\textbf{Your answer:} $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .\\

\vspace*{2.2in}

\paragraph{2.} Perform the indicated operation and simplify.
\[
\frac{1}{x+3} - \frac{3}{x^2+5x+6}
\]

\ni
\textbf{Your answer:} $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .\\


\newpage
\paragraph{3.} Simplify
\[
\frac{\frac{6}{x}+\frac{3}{x^2}}{\frac{3}{x}+1}
\]

\ni
\textbf{Your answer:} $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .\\
\vspace*{3.8in}


\paragraph{4.} Solve for $x$.
\[
\frac{5}{x+5} = \frac{3x}{x+5} + 2
\]

\ni
\textbf{Your answer:} $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .

\newpage
\paragraph{5.} Simplify:
\(
\sqrt{12} + \sqrt{48} - 2 \sqrt{20}
\)
\hspace{2.5cm}
\textbf{Your answer:} $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .
\vspace*{4.0in}

\paragraph{6.} Simplify:
\[
\left (\frac{x^{1/2}y^{2/3}}{x^{1/3}y^{-1/4}}\right )^{12}
\]

\ni
\textbf{Your answer: } $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .

\newpage
\paragraph{7.} Rationalize the denominator and simplify.
\[
\frac{3}{2\sqrt{3} - 5}
\]

\ni
\textbf{Your answer:} $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .

\vspace*{3.8in}

\paragraph{8.} Solve for $y$:
\(
\sqrt{3y+4} = 7
\)
\hspace{2.7cm}
\textbf{Your answer: } $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .

\newpage
\paragraph{9.} Express the following in simplest radical form. \\
(a) $\sqrt{54x^7y^6}$
\hspace{4.7cm}
\textbf{Your answer:} $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .
\vspace*{2.2in}

\noindent
(b)
$\sqrt[3]{54x^7y^6}$
\hspace{4.0cm}
\textbf{Your answer: } $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .

\vspace*{2.2in}


\noindent
(c) 
$(\sqrt{7a})^2$
\hspace{4.0cm}
\textbf{Your answer: } $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .

\vspace*{2.2in}

\noindent
(d) 
$(7\sqrt{a})^2$
\hspace{4.0cm}
\textbf{Your answer: } $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ .

%\vspace*{3.2in}

\newpage
\paragraph{10.} Evaluate 
$(16^{-1/2})(27^{2/3})$
\hspace{3.3cm}
\textbf{Your answer: } $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

\end{document}