Bepaal die waarde van y en kies die regte antwoord: \( \frac{{2x}}{{{x^2} - 2x - 8}} - \frac{5}{{4 - x}} = \frac{3}{{2 + x}} \)
\( \begin{align} \frac{{2x}}{{{x^2} - 2x - 8}} - \frac{5}{{4 - x}} &= \frac{3}{{2 + x}}\\ \frac{{2x}}{{\left( {x - 4} \right)\left( {x + 2} \right)}} + \frac{5}{{\left( {x - 4} \right)}} &= \frac{3}{{\left( {x + 2} \right)}}\\ KGV &= \left( {x - 4} \right)\left( {x + 2} \right) \\ 2x + 5\left( {x + 2} \right) &= 3\left( {x - 4} \right)\\ 2x + 5x + 10 &= 3x - 12\\ 2x + 5x - 3x &= - 12 - 10\\ 4x &= - 22\\ x &= - \frac{{11}}{2} \end{align} \)
Beperkings:
\( \begin{align} x - 4 &\ne 0\\ x &\ne 4 \end{align} \)
\( \begin{align} x + 2 &\ne 0\\ x &\ne - 2 \end{align} \)