evaluate the limit as x approaches positive and negative infinity (x^2+6x+8)/(x+3)^2
factor:
(x+4)(x+2)/(x+3)(x+3)
divide numerator and denominator by x^2
(1+4/x)(1+2/x)/(1+3/x)(1+3/x)
now as x >>inf
all of the fractions go to zero, leaving....