Verified answer

f(x) =  (2x² + 3x - 5)/(x² + 4x - 5)

сделаем сначала x->∞  lim(x->∞)  (2x² + 3x - 5)/(x² + 4x - 5) = делим на х² числитель и знаменатель =  lim(x->∞)  (2 + 3/x - 5/x²)/(1 + 4/x - 5/x²)  = (2 + 0 - 0)/(1 + 0 - 0) = 2

теперь разложим числитель и знаменатель

2x² + 3x - 5 = 2(x + 5/2)(x - 1) = (2x + 5)(x - 1)

D = 9 + 40 = 49

x12 = (-3 +- 7)/4 = -5/2  1

x² + 4x - 5 = (x - 1)(x + 5)

D = 16 + 20 = 36

x12 = (-4 +- 6)/2 = -5   1

итак получили f(x) = (2x + 5)(x - 1)/(x - 1)(x + 5) = (2x + 5)/(x + 5)

1/  x->1 (2x + 5)(x - 1)/(x - 1)(x + 5) = (2x + 5)/(x + 5) = (2 + 5)/(1 + 5) = 7/6

2/ x->-5 (2x + 5)(x - 1)/(x - 1)(x + 5) = (2x + 5)/(x + 5)=(-10 + 5)/(-5+5) = -5/0=-∞

3/ x->-1 (2x + 5)(x - 1)/(x - 1)(x + 5) = (2x + 5)/(x + 5)=(-2+5)/(-1 + 5) = 3/4

4/ x->2/5 (2x + 5)(x - 1)/(x - 1)(x + 5) = (2x + 5)/(x + 5)=(4/5 + 5)/(2/5 + 5) = 29/5 : 12/5 = 29/12

вероянее -5/2 было тогда (2x + 5)(x - 1)/(x - 1)(x + 5) = (2x + 5)/(x + 5) = (-5 + 5)/(-5/2 + 5) = 0/5/2 = 0

5/ x-> ∞ (2x + 5)(x - 1)/(x - 1)(x + 5) = (2x + 5)/(x + 5) = (2 + 5/x)/(1 + 5/x) = 2