It appears that you found the least common multiple (LCM) of the denominators, but then subtracted the given numerators. First rewrite each fraction with the LCM as the denominator:

$\displaystyle\frac{{{3}{x}-{2}}}{{{x}-{2}}}-\frac{{{x}-{1}}}{{{{x}}^{{2}}-{5}{x}+{6}}}=\frac{{{\left({3}{x}-{2}\right)}{\left({x}-{3}\right)}}}{{{\left({x}-{2}\right)}{\left({x}-{3}\right)}}}-\frac{{{x}-{1}}}{{{\left({x}-{2}\right)}{\left({x}-{3}\right)}}}\usepackage{cmbright}\Huge\$

Then subtract and simplify.