# Construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2. Explain how you determined your answer.

Construct a rational function that has a vertical asymptote at $x=3$ and a removable discontinuity at $x=-2$.
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doplovif
Since $x=3$ is a vertical asymptote, then $x-3$ is a factor in the denominator. Since there is a removable discontinuity at $x=-2$, then $x+2$ is a common factor in the numerator and denominator. So, a possible rational function is:
$f\left(x\right)=\frac{x+2}{\left(x-3\right)\left(x+2\right)}$
or
$f\left(x\right)=\frac{x+2}{{x}^{2}-x-6}$