3. Let $\alpha$ be an acute angle, $x=\frac{\sqrt{\sin \alpha}+\sqrt{\cos \alpha}}{\sqrt{\sin \alpha+\cos \alpha}}$, $y=\sqrt{\sin \alpha+\cos \alpha}$, $z=\frac{2 \sin \alpha \cdot \cos \alpha}{\sin \alpha+\cos \alpha}$.
Then the order of magnitude of $x$, $y$, and $z$ is ( ).
(A) $x \geqslant y \geqslant z$
(B) $x \geqslant z \geqslant y$
(C) $z \geqslant x \geqslant y$
(D) $z \geqslant y \geqslant x$
3. A.
$$
\begin{array}{l}
\frac{x}{y}=\frac{\sqrt{\sin \alpha}+\sqrt{\cos \alpha}}{\sin \alpha+\cos \alpha} \geqslant \frac{\sin \alpha+\cos \alpha}{\sin \alpha+\cos \alpha}=1, \\
z=\frac{2 \sin \alpha \cdot \cos \alpha}{\sin \alpha+\cos \alpha} \leqslant \frac{2 \sin \alpha \cdot \cos \alpha}{2 \sqrt{\sin \alpha \cdot \cos \alpha}} \\
=\sqrt{\sin \alpha \cdot \cos \alpha}<\sqrt{\sin \alpha+\cos \alpha}=y .
\end{array}
$$

Therefore, \( x \geqslant y \geqslant z \).