Oscillation of first order neutral differential equations with positive and negative coefficients

We obtain some new sharp sufficient conditions for the oscillation of all solutions of the first order neutral differential equation with positive and negative coefficients of the form $$\frac{d}{dt}\bigl(x(t) - R(t)x(t - r)\bigr)+ P(t)x(t - \tau ) - Q(t)x(t -\delta) = 0$$ where $P,Q,R\in C([t_0,\infty),R^^), r\in (0,\infty)$ and $\tau,\delta\in R^+$. In particular, the conditions are necessary and sufficient when the coefficients are constants. As corollaries, many known results are extended and improved in the literature.