# 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 $$B_t = -x$$?