Create a rational function that meets the given criteria:

Question

• Numerator is a quadratic function with a x-intercept at x=-2
• denominator is a cubic function
• There must be only one removable discontinuity at x=3
• There must be 2 infinite discontinuities at x=-1 and x=2

Answer 1

(x+2)(x-3)/(x-3)(x+1)(x-2)=(x+2)(x-3)/(x-3)(x^2-x-2)=

(x+2)(x-3)/(x^3-4x^2+x+6)

= (x^2 -x-6)/(x^3-4x^2+x+6)