Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$ Using the equivalency, I got the answer equal to $1$, however the answer is given as $\frac34$. 
WolframAlpha also gives $\frac34$.
Could someone tell me that the given answer is wrong or I made a mistake!

Substitute $x=1/t$; then, with a simple massage, the limit becomes
$$
\lim_{t\to0^+}
  \frac{\sqrt{1+t}+\sqrt{1+2t}-2\sqrt{1+3t}}
       {\sqrt{1+2t}+1-2\sqrt{1+3t}}
=\lim_{t\to0^+}
  \frac{(1+\frac{1}{2}t)+(1+t)-2(1+\frac{3}{2}t)+o(t)}
       {(1+t)+1-2(1+\frac{3}{2}t)+o(t)}=
\frac{-3/2}{-2}=\frac{3}{4}
$$
using the first order Taylor expansion.
