It seems you want to simplify the rational function:
f(x) = (2x + 1) / [(2x + 2)(2x + 6)]
You can start by factoring the numerator and the denominator:
f(x) = [(2x + 1)] / [(2x + 2)(2x + 6)]
Now, let's simplify further. The numerator is already factored. In the denominator, you can factor out a 2 from both terms:
f(x) = [(2x + 1)] / [2(2x + 1)(x + 3)]
Now, you can see that there's a common factor of (2x + 1) in both the numerator and the denominator. Cancel out this common factor:
f(x) = 1 / [2(x + 3)]
So, the simplified form of the function is:
f(x) = 1 / [2(x + 3)]