Doing so requires a lot of calculation and trouble. You should use interception.

Let A(a, 0), B(0, b) (a >; 0，b & gt0)

Then 3/a+2/b =1>; =2√(3/a*2/b)=2√(6/ab)

So ab & gt=24, if and only if a=6 and b=4, ab takes the minimum value of 24.

Therefore, when a=6 and b=4, the area of △AOB is the smallest, which is 1/2*ab= 12.

At this time, the equation of the straight line is x/6+y/4= 1, that is, 2x+3y= 12.