Rewrite

20x222x+234x2+5x5\displaystyle \frac{{-{20}{x}^{{2}}-{22}{x}+{23}}}{{{4}{x}^{{2}}+{5}{x}-{5}}}

in the form

q(x)+r(x)4x2+5x5\displaystyle {q}{\left({x}\right)}+\frac{{{r}{\left({x}\right)}}}{{{4}{x}^{{2}}+{5}{x}-{5}}}.

20x222x+23\displaystyle -{20}{x}^{{2}}-{22}{x}+{23} =\displaystyle = +\displaystyle +
4x2+5x5\displaystyle {4}{x}^{{2}}+{5}{x}-{5} 4x2+5x5\displaystyle {4}{x}^{{2}}+{5}{x}-{5}