a+1 ÷ a2+2a+1
If you factor a² + 2a + 1, you get (a+1)(a+1).
Now the problem is: (a+1) / [ (a+1)(a+1) ].
Cancel the (a + 1) in the numerator with one of the (a + 1)'s in the denominator, you have;
1 / (a + 1)