Question

find the vertical asymptotes and holes.

y= x+5/x^2+9 (its a fraction)

Answer 1

Vertical asymptotes and holes both occur when the denominator is zero at a point.
We'd set the denominator equal to 0 and find the x-values: \( x^2 + 9 = 0 \).

Holes occur when the numerator and denominator both contain the same factors and there are enough to cancel each-other out evenly (ex. if the denominator had (x-2)^2 and the numerator only had (x-2), then it would not be a hole). Otherwise, the point in the denominator is an asymptote.