Bepaal y en kies die regte antwoord \( {y^2} - 3y + \frac{{40}}{{y\left( {y - 3} \right)}} = 14 \)

\( \begin{align} {y^2} - 3y + \frac{{40}}{{y\left( {y - 3} \right)}} &= 14\\ {y^2} - 3y + \frac{{40}}{{{y^2} - 3y}} &= 14\\ {\rm{Stel }}\,\,\,k &= {y^2} - 3y\\ k + \frac{{40}}{k} &= 14\\ KGV = k;\,\,&BPK:k \ne 0\\ {k^2} + 40 &= 14k\\ {k^2} - 14k + 40 &= 0\\ \left( {k - 10} \right)\left( {k - 4} \right) &= 0\\ k = 10\,\,\,{\rm{ of}}\,\,\,k &= 4\\ {\rm{maar }}\,\,\,k &= {y^2} - 3y\\ {y^2} - 3y& = 10 &of& &{y^2} - 3y &= 4\\ {y^2} - 3y - 10 &= 0 & & &{y^2} - 3y - 4 &= 0\\ \left({y - 5}\right)\left({y + 2}\right) &= 0 && &\left( {y - 4} \right)\left( {y + 1} \right) &= 0\\ y = 5\,\,\,{\rm{of}}\,\,\,y &= - 2 && &y = 4\,\,\,{\rm{of}}\,\,\,y &= - 1 \end{align} \)