Please let me know what is wrong in the following algebraic simplification which gives a wrong limit value.

$$\lim\_{x \to \infty} (\sqrt {x^2 - 4x} - x)=\lim\_{x \to \infty} (\sqrt {x^2 (1 - 4/x)} - x) $$  

$$= \lim\_{x \to \infty} (x\sqrt {1 - 4/x} - x)= \lim\_{x \to \infty} x(\sqrt {1 - 4/x} - 1) $$ 

When $x$ tends to infinity, $4/x$ will be negligible and hence

$$= \lim\_{x \to \infty} x(\sqrt {1 - 0} - 1)=\lim\_{x \to \infty} x(1 - 1)=0 $$