Answer:
Option 3) [tex]\frac{1}{(t+4)^{2}}[/tex]
Step-by-step explanation:
In the given question we have to calculate the quotient after division.
To solve this question we will factorize (t²+7t+12) first and then we will will divide by this.
⇒ t²+7t+12 = ( t²+4t+3t+12)
⇒ t(t+4)+3(t+4)
⇒ (t+3)(t+4)
Now its a simpler form of divisor to get the answer.
We come back to the question
[tex]\frac{(t+3)}{t+4}\div(t^{2}+7t+12)[/tex]
[tex]= \frac{(t+3)}{t+4}\div(t+3)(t+4)[/tex]
Or [tex]=\frac{(t+3)}{t+4}\times\frac{1}{(t+3)(t+4)}[/tex]
[tex]=\frac{1}{(t+4)^{2}}[/tex]
So the right answer is [tex]\frac{1}{(t+4)^{2}}[/tex]
