Answer:
Third option is correct: 1 / (t+4)^2
Explanation:
This equation can be written as the following:
(t+3)/(t+4)*(1/t^2+7t+12)
We know this because of the division of fractions. For example:
(1/y)/(1/x) = (1/y)*(x/1)
Now that we know this, we can advance.
Now we have to try to factor (t^2+7t+12)
We can make this into (t+3)(t+4)
Ah! Perfect! There is a t+3 in the denominator of the first fraction!
We can now cancel these out.
Now our equation looks like this:
(1 / t+4) * (1 / t+4)
This can also be written as 1^2 / (t+4)^2 = 1 / (t+4) ^2
So the correct option is the third one.