Answer
$y=\frac{(x-1)(x-3)(x^2+\frac{4}{3})}{(x+1)^2(x-2)^2}$.
Work Step by Step
Step 1. Identify asymptote(s): V.A. $x=-1,2$, H.A. $y=1$,
Step 2. Identify zero(s): $x=1,3$,
Step 3. Write a general form $y=\frac{(x-1)(x-3)(x^2+a)}{(x+1)^2(x-2)^2}$,
Step 4. Use point $(0,2)$, we have $a=\frac{(1)^2(-2)^2}{(-1)(-3)}=\frac{4}{3}$,
Step 5. Provide one solution $y=\frac{(x-1)(x-3)(x^2+\frac{4}{3})}{(x+1)^2(x-2)^2}$.
