Walker and Saw (1978) derived the distribution of an arbitrary linear combination of student's random variables with odd degrees of freedom. An extension to the case of any degrees of freedom is demonstrated in this paper. The proposed procedure uses approximation of the characteristic function of the student's t distribution given by Saleh (1994). For the special case of the sum or the difference of two independent t-variables, our approximation is compared with the exact probability given earlier by Ghosh (1975), and good results are obtained.