Question

What is the quotient?

Answer 1

Option 3)
`(1)/((t+4)^(2))`

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

`((t+3))/(t+4)/(t^(2)+7t+12)`

`= ((t+3))/(t+4)/(t+3)(t+4)`

Or
`=((t+3))/(t+4)*(1)/((t+3)(t+4))`

`=(1)/((t+4)^(2))`

So the right answer is
`(1)/((t+4)^(2))`