Solution
Step 1:
Write the rational expression:
[tex]\begin{gathered} f(x)\text{ = }\frac{x+4}{x^2+5x-24} \\ \end{gathered}[/tex]
Step 2:
Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).
Step 3
[tex]\begin{gathered} x^2+5x-24=0 \\ \\ x^2+8x\text{ - 3x - 24 = 0} \\ \\ x(x\text{ + 8\rparen-3\lparen x + 8\rparen = 0} \\ \\ (x\text{ - 3\rparen\lparen x + 8\rparen = 0} \\ \\ x\text{ - 3 = 0, x + 8 = 0} \\ x\text{ = 3, x = -8} \end{gathered}[/tex]
Step 4:
\ertical} Asymptote is =-8,\ =3,
