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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 $B_t = -x$?