3. `y=(x+2)/(x^2+2x-8)`, find Asymptotes of a function

Solution:
Asymptotes :
Now, find domain of `y=(x+2)/(x^2+2x-8)`

`y=(x+2)/(x^2+2x-8)`

`x^2+2x-8=0`

`=>x^2+2x-8=0`

`=>x^2-2x+4x-8 = 0`

`=>x(x-2)+4(x-2) = 0`

`=>(x-2)(x+4) = 0`

`=>(x-2) = 0" or "(x+4) = 0`

`=>x = 2" or "x = -4`

Domain : `x!=2,x!=-4`

Vertical asymptote : `x=2,x=-4`

The highest power in the numerator is 1
The highest power in the denominator is 2
Since highest power denominator is greater than highest power on numerator, then the horizontal asymptote will be x-axis.
Horizontal asymptote : y = 0 (x-axis)
Slant(Oblique) asymptote : none

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