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%TCIDATA{<META NAME="Title" CONTENT="Compute in Place">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Wed May 14 11:46:53 1997}
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\input{tcilatex}
\begin{document}


\subsection{Compute in Place\label{Compute in Place}\hrulefill}

You can use many Maple commands to compute in place, replacing part of an
expression with the result of a Maple operation. With compute in place, you
can demonstrate the steps involved in a problem solution.

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Simplify $%
\dfrac{x+2}{x+1}+\dfrac{3x}{x-1}$}

\begin{enumerate}
\item  Click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{fraction.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 19.5625pt;height 18.8125pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'fraction.wmf';file-properties "XNPEU";}}or,
from the Insert menu, choose Fraction.

\item  Type \textbf{x+2}, press Tab, type \textbf{x+1},\textbf{\ }and press
spacebar.

\item  Type \textbf{+ }, click\FRAME{itbpF}{19.5625pt}{18.8125pt}{2pt}{}{}{%
fraction.wmf}{\special{language "Scientific Word";type "GRAPHIC";display
"PICT";valid_file "F";width 19.5625pt;height 18.8125pt;depth
2pt;original-width 17.8125pt;original-height 16.9375pt;cropleft "0";croptop
"1";cropright "1";cropbottom "0";filename 'fraction.wmf';file-properties
"XNPEU";}}, type \textbf{3x}, press Tab, and type \textbf{x-1}.

\item  Click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{simplify.wmf}{%
\special{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
17.8125pt;original-height 16.9375pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'simplify.wmf';file-properties "XNPEU";}}or,
from the Maple menu, choose Simplify. Maple returns this result: $\dfrac{x+2%
}{x+1}+\dfrac{3x}{x-1}=\allowbreak 2\dfrac{2x^{2}+2x-1}{\left( x+1\right)
\left( x-1\right) }.$\medskip 

\item  Select the denominator in the answer, hold down the Ctrl key, and
click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{expand.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
20.3125pt;original-height 18.8125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'expand.wmf';file-properties "XNPEU";}}. On your
screen, you see this result: \ 
\[
\fbox{%
\begin{tabular}{lll}
\rule[-0.15in]{0in}{0.4in} & $\dfrac{x+2}{x+1}+\dfrac{3x}{x-1}=\allowbreak 2%
\dfrac{2x^{2}+2x-1}{x^{2}-1}$ & \rule[-0.15in]{0in}{0.4in}%
\end{tabular}
}
\]
\medskip 
\end{enumerate}

\subparagraph{\FRAME{itbpF}{50.75pt}{21.75pt}{6pt}{}{}{ex3.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid-file
"F";width 50.75pt;height 21.75pt;depth 6pt;original-width
48.875pt;original-height 19.5625pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'ex3.WMF';file-properties "XNPEU";}}Simplify $%
\dfrac{x+2}{x+1}+\dfrac{3x}{x-1}$ and show the steps in the solution}

\begin{enumerate}
\item  Follow steps 1--3 in the previous example to enter and simplify the
expression.

\item  Type \textbf{=} .

\item  Select the answer returned by Maple.

\item  Hold down the Ctrl key and drag a copy of the answer to the right of
the equals sign.

\item  Select the denominator in the copied answer, hold down the Ctrl key,
and click\FRAME{itbpF}{22.4375pt}{21.0625pt}{2pt}{}{}{expand.wmf}{\special%
{language "Scientific Word";type "GRAPHIC";display "PICT";valid_file
"F";width 22.4375pt;height 21.0625pt;depth 2pt;original-width
20.3125pt;original-height 18.8125pt;cropleft "0";croptop "1";cropright
"1";cropbottom "0";filename 'expand.wmf';file-properties "XNPEU";}}or, from
the Maple menu, choose Expand. Now you see all the steps in the solution: \
\medskip 
\[
\fbox{%
\begin{tabular}{lllll}
\rule[-0.15in]{0in}{0.4in} &  & $\dfrac{x+2}{x+1}+\dfrac{3x}{x-1}%
=\allowbreak 2\dfrac{2x^{2}+2x-1}{\left( x+1\right) \left( x-1\right) }%
=\allowbreak 2\dfrac{2x^{2}+2x-1}{x^{2}-1}$ & \rule[-0.15in]{0in}{0.4in} & 
\end{tabular}
}
\]
\medskip \medskip 
\end{enumerate}

\subparagraph{Compute in place to show the steps in the solution of these
problems\protect\medskip \textit{\label{exercises}}}

\begin{quotation}
\qquad Combine $\dfrac{x}{x-y}-\dfrac{x^{2}}{x^{2}-y^{2}}$ to give $\dfrac{xy%
}{\left( x-y\right) \left( x+y\right) }.$\medskip 

\qquad Combine these fractions $\dfrac{x}{x+3}-\dfrac{6x+6}{x^{2}-9}+\dfrac{%
x+1}{x-3}$ and simplify to $\dfrac{2x+1}{x+3}.$
\end{quotation}

\end{document}
