Решение
lim x--> 4 [(2x² - 5x - 12) / (x² + x - 20)] ;
1) 2x² - 5x - 12 = 0
D = 25 + 4*2*12 = 121
x₁ = (5 - 11)/4
x₁ = - 1,5
x₂ = (5 + 11)/4
x₂= 4
2x² - 5x - 12 = 2*(x + 1,5)*(x - 4)
2) x² + x - 20 = 0
x₁ = - 5
x₂ = 4
x² + x - 20 = (x + 5)*(x - 4)
= lim x--> 4 [2*(x + 1,5)*(x - 4)] / [(x + 5)*(x - 4)] =
= lim x--> 4 (2x + 3) / (x + 5) = (2*4 + 3)/(4 + 5) = 11/9 = 1 (2/9)