若(9m+1)的2次方=3的16次方,求正整数m的值

令a=(x+2)/(x2+3)
则4a=1/a-3
4a2+3a-1=0
(4a-1)(a+1)=0
a=1/4,a=-1
(x+2)/(x2+3)=1/4
x2+3=4x+8
x2-4x-5=0
x=5,x=-1
(x+2)/(x2+3)=-1
x2+3=-x-2
x2-x+5=0
无解
所以x=5,x=-1