Explain a math problem-the finale of multiple-choice questions in the simulated test paper for senior high school entrance examination (difficulty level: "I can't")

y=(6x + 3)/(2x - 1)

=[3(2x - 1)+6]/(2x - 1)

=3+6/(2x - 1)

Therefore, the image of the function y=3+6/(2x- 1) is symmetrical about the center of the point (1/2,3).

For the value of y to be an integer, 6/(2x- 1) must be an integer.

That is, (2x- 1) is divisible by 6, because (2x- 1) is an odd number.

So (2x- 1) can only take -3,-1, 1, 3.

1. When 2x- 1=-3, x=- 1, y= 1, the point is (-1, 1).

2. When 2x- 1=- 1, x=0 and y=-3, the point is (0, -3).

3. When 2x- 1= 1, x= 1 and y=9, the point is (1, 9).

4. When 2x- 1=3, x=2, y=5, the point is (2,5).

So a * * * has only four whole points, and there are (-1, 1) and (2,5), (0,3) and (1, 9).

They are symmetric about the center of (1/2,3) respectively.