write a possible equation for a rational function with a hole at x=2 and a vertical asymptote at x=-3 and at least one zero

Question

A hole in a rational function at x=2 means

Answer 1

f(x) = (x-2)(x+5) / (x-2)(x+3) or multiplied out f(x) = (x²+3x-10) / (x²+x-6).

 

x=2 is a hole because it leads to zeros in both the numerator and denominator while x=-3 is an asymptote since it makes only the denominator zero.

 

The x=-5 is the only number which makes the fraction zero since the numerator will be zero.

Hope this helped