I want to create a table like this in LaTeX:

How would I do that?
I want to create a table like this in LaTeX:

How would I do that?
Just a bit of patience in removing the unwanted rules. The gap for getting the fraction not to touch the rule is obtained by an invisible rule (I'd use the slashed form, by the way).
\documentclass{article}
\begin{document}
\[
\begin{array}{l|c|rr|c|c|}
\multicolumn{2}{c}{} & % omit the vertical lines
\multicolumn{1}{c}{x_1} &
\multicolumn{1}{c}{\mbox{\boldmath$x_6$}} &
\multicolumn{2}{c}{} \\
\cline{2-5}
& -1 & 1 & 3 & 0 & \multicolumn{1}{c}{} \\
\cline{2-6}
\mbox{\boldmath$x_1$}
& 1 & 7 & 2 & 5 & \rule{0pt}{1.2\ht\strutbox}\frac{5}{2} \\[1ex]
x_2
& 0 & 1 & -6 & 9 & - \\[1ex]
x_3
& 2 & -10 & 4 & 20 & 5 \\[1ex]
x_4
& 3 & -1 & 0 & 8 & - \\
\cline{2-6}
\multicolumn{2}{c|}{}
& -17 & 13 & 69 & \multicolumn{1}{c}{} \\
\cline{3-5}
\end{array}
\]
\end{document}

A solution with blkarray:
% arara: pdflatex
\documentclass{article}
\usepackage{blkarray}
\usepackage{bm}
\begin{document}
\[
\renewcommand{\arraystretch}{1.1}
\begin{blockarray}{l*{5}{r}} % for your image, you will have to change column 2, 5, and 6 to `c` in all blocks.
& & x_5&\boldsymbol{x_6}&\\\cline{2-5}
\begin{block}{l|r|rr|r|r}
\null& -1 & 1 & -3 & 0 &\\
\end{block}\cline{2-6}
\begin{block}{l|r|rr|r|r|}
\boldsymbol{x_1} & 1 & 7 & 2 & 5 & \frac{5}{2}\\
x_2 & 0 & 1 & -6 & 9 & -\\
x_3 & 2 & -10 & 4 & 20 & 5\\
x_4 & 3 & -1 & 0 & 8 & -\\
\end{block}\cline{2-6}
\begin{block}{lr|rr|r|r}
\null& \null & -17 & 13 & 69 &\\
\end{block}\cline{3-5}
\end{blockarray}
\]
\end{document}

With a tabular
\documentclass{article}
\usepackage{array,bm}
\newcolumntype{R}{>{$}r<{$}}
\newcolumntype{C}{>{$}c<{$}}
\renewcommand{\arraystretch}{1.2}
\begin{document}
\begin{tabular}{C|C|RR|C|C|}
\multicolumn{2}{c}{} & x_5 & \multicolumn{1}{r}{$\bm{x_6}$} \\
\cline{2-5}
& -1 & 1 & -3 & 0 \\
\cline{2-6}
\bm{x_1} & 1 & 7 & 2 & 5 & \frac{5}{2} \\
x_2 & 0 & 1 & -6 & 9 & - \\
x_3 & 2 & -10 & 4 & 20 & 5 \\
x_4 & 3 & -1 & 0 & 8 & - \\
\cline{2-6}
\multicolumn{2}{c|}{} & -17 & 13 & 69 \\
\cline{3-5}
\end{tabular}
\end{document}
