Question

What is the limit of `[(x^2) + 5x + 4] / [(x^2) + 3x -4]` as x approaches -4?

Answer 1

`3/5.`

Explanation:

`"The Nr.="x^2+5x-4=(x+4)(x+1).`

`"The Dr.="x^2+3x-4=(x+4)(x-1)`.

Therefore, the Limit`=lim_(x to -4) {(cancel(x+4))(x+1)}/{(cancel(x+4))(x-1)}`

`=lim_(x to -4) (x+1)/(x-1)`

`=(-4+1)/(-4-1)=(-3)/(-5)`

`=3/5`.