\begin{matrix} VT=\frac{(mbc+n)(b-c)+(mac+n)(c-a)+(mab+n)(a-b)}{-(a-b)(b-c)(c-a)} & \\ =\frac{mb^{2}c-mbc^{2}+nb-nc+mac^{2}-ma^{2}c+nc-na+ma^{2}b-mab^{2}}{-(a-b)(b-c)(c-a)} & \end{matrix}\begin{matrix} =\frac{m(b^{2}c-bc^{2}+ac^{2}-a^{2}c+a^{2}b-ab^{2}}{-(a-b)(b-c)(c-a)} & \\ =\frac{-m(a-b)(b-c)(c-a)}{-(a-b)(b-c)(c-a)}=m & \end{matrix}