jmc

First, we convert the following numbers to base 10: $$1357_9=7\cdot 9^0+5\cdot 9^1+3\cdot 9^2+1\cdot 9^3=7+45+243+729=1024_{10},$$$$100_4=0\cdot 4^0+0\cdot 4^1+1\cdot 4^2=16_{10},$$$$2460_8=0\cdot 8^0+6\cdot 8^1+4\cdot 8^2+2\cdot 8^3=48+256+1024=1328_{10},\text{and}$$$$5678_9=8\cdot 9^0+7\cdot 9^1+6\cdot 9^2+5\cdot 9^3=8+63+486+3645=4202_{10}.$$So the original expression equals $\frac{1024}{16}-1328+4202=\boxed{2938}.$