\ANG{
Berechne die L"osungsmenge:\qquad
$\D\sqrt{x+5}=\sqrt{x-3}+\sqrt{x-2}$
}
\LSG{
$x>3\quad\DANN\quad\DD=[3,+\infty[$
\begin{align}
  x+5&=x-3+x-2+2\sqrt{x^{2}-5x+6}\nonumber\\
  10-x&=2\sqrt{x^{2}-5x+6}\nonumber\\
  100-20x+x^{2}&=4x^{2}-20x+24\nonumber\\
  x^{2}&=\frac{76}{3}\quad\DANN\quad x_{1}=\frac23\sqrt{57}\approx 5{,}03,\quad
  \left(x_{2}=-\frac23\sqrt{57}\notin\DD\right)\nonumber
\end{align}
}
