lim 2t+4/ 12-3t^2 as t approaches -2

Question

Its about limit, and i dont understand how to get this answer. help 

Answer 1

Let's rewrite your expression:

 

                       2t+4/(12 -3t^2) = 2(t+2)/3(4 - t^2) = 2(t+2)/3(2-t)(2+t) = 2/3(2-t).

 

Thus, when t approaches -2 your limit will be 2/12 = 1/6.

Answer 2

First, you need to factor the numerator and denominator as much as possible. The top can be factored into 2(t+2) and the denominator can be factored into 3(4-t²), which further factors into 3(2-t)(2+t). The (t+2) can be canceled out in the numerator and denominator, leaving the following: 2/(3(2-t)). Now we can plug in -2 into this equation and we get 2/(3*4), or 1/6.