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High school mathematics Olympics
I'll just talk about a few key steps on this topic, so I won't write the process in detail.

1/a+b = a+b+c/a+b =1+c/a+b, others are also deformations.

Square of A+b+c= 1 Then, the square average is greater than the arithmetic average, and 6(ab+bc+ca) is greater than or equal to 2.

Because a and a, b.c are positive numbers, and then using the reciprocal property, such as a+b/b+c+b+c/a+b is greater than or equal to 2, the other two formulas are also written. When the three formulas are added together, 2a/b+c +2b/a+c +2c/a+b is greater than or equal to 3.

In the end, we will come to a conclusion.

Some symbols can't be typed, so you can only write them like this. If you are careful, you will understand.