So sánh a = 9^2009+1/9^2010+1 và b = 9^2010-2/9^2011-2

To simplify the expressions, we can rewrite them as follows:

a = (9^2009 + 1) / (9^2010 + 1)
b = (9^2010 - 2) / (9^2011 - 2)

Let's simplify each expression separately:

For a:
We can notice that 9^2009 + 1 is a sum of two terms. We can use the formula for the sum of two cubes to simplify it further:
a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, a = 9^669 and b = 1. So we have:
9^2009 + 1 = (9^669 + 1)(9^1338 - 9^669 + 1)

Now, let's simplify the denominator:
9^2010 + 1 = (9^670 + 1)(9^1339 - 9^670 + 1)

Therefore, a = (9^669 + 1)(9^1338 - 9^669 + 1) / (9^670 + 1)(9^1339 - 9^670 + 1)

For b:
We can use the same approach as above to simplify the numerator and denominator separately:
9^2010 - 2 = (9^670 - 2)(9^1340 + 9^670 + 1)
9^2011 - 2 = (9^671 - 2)(9^1341 + 9^671 + 1)

Therefore, b = (9^670 - 2) / (9^671 - 2)(9^1341 + 9^671 + 1)

So the simplified expressions for a and b are:

a = (9^669 + 1)(9^1338 - 9^669 + 1) / (9^670 + 1)(9^1339 - 9^670 + 1)
b = (9^670 - 2) / (9^671 - 2)(9^1341 + 9^671 + 1)