\(\displaystyle\frac{{5}}{{{y}-{4}}}={3}\frac{{y}}{{{y}+{2}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{y}^{{2}}–{2}{y}–{8}}}\)

\(\displaystyle\frac{{5}}{{{y}-{4}}}={3}\frac{{y}}{{{y}+{2}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{\left({y}–{4}\right)}{\left({y}–{2}\right)}}}\)

\(\displaystyle\frac{{{5}{\left({y}+{2}\right)}}}{{{\left({y}-{4}\right)}{\left({y}+{2}\right)}}}=\frac{{{3}{y}{\left({y}–{4}\right)}}}{{{\left({y}+{2}\right)}{\left({y}-{4}\right)}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{\left({y}–{4}\right)}{\left({y}–{2}\right)}}}\)

\(\displaystyle{5}{y}+{10}={3}{y}^{{2}}–{12}{y}–{2}{y}^{{2}}+{14}{y}\)

\(\displaystyle-{y}^{{2}}+{3}{y}+{10}={0}\)

\(\displaystyle{y}^{{2}}–{3}{y}–{10}={0}\)

\(\displaystyle{\left({y}–{5}\right)}{\left({y}+{2}\right)}={0}\)

\(\displaystyle{y}={5}{\quad\text{or}\quad}{y}=-{2}\)

\(\displaystyle\frac{{5}}{{{y}-{4}}}={3}\frac{{y}}{{{y}+{2}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{\left({y}–{4}\right)}{\left({y}–{2}\right)}}}\)

\(\displaystyle\frac{{{5}{\left({y}+{2}\right)}}}{{{\left({y}-{4}\right)}{\left({y}+{2}\right)}}}=\frac{{{3}{y}{\left({y}–{4}\right)}}}{{{\left({y}+{2}\right)}{\left({y}-{4}\right)}}}–\frac{{{2}{y}^{{2}}–{14}{y}}}{{{\left({y}–{4}\right)}{\left({y}–{2}\right)}}}\)

\(\displaystyle{5}{y}+{10}={3}{y}^{{2}}–{12}{y}–{2}{y}^{{2}}+{14}{y}\)

\(\displaystyle-{y}^{{2}}+{3}{y}+{10}={0}\)

\(\displaystyle{y}^{{2}}–{3}{y}–{10}={0}\)

\(\displaystyle{\left({y}–{5}\right)}{\left({y}+{2}\right)}={0}\)

\(\displaystyle{y}={5}{\quad\text{or}\quad}{y}=-{2}\)