stochastic processes – Local Martingale but not Martingale

For a 3-dimensional Brownian motion $B = (B_t, t ≥ 0)$ and $x ∈ mathbb{R}^3 backslash {0}$ define the process
$Y = (Y_t, t ≥ 0)$ via $Y_t =frac{1}{|B_t+x|}$ how come this is a continuous local martingale but not proper martingale? and is it possible to deduce continuity from of $Y$ from the continuity of the brownian motion? I suspect this could get difficult when $B_t = -x$?