（4a+9b)/(ab)
=（4a+9b)(a+b)/(ab)
=(4a^+13ab+9b^)/(ab)
=4a/b+9b/a+13
>=12+13
=25,
∴ab/(4a+9b)<=1/25,
当4a/b=9b/a,a+b=1,即a=3/5,b=2/5时取等号,
∴ab/(4a+9b)的最大值=1/25.