Question

lim x->(-5) (2x^2+15x+25)/(5-4x-x^2)

Answer 1

limx->-5 (2x^2+15x+25)/(5-4x-x^2)

Разложим числитель и знаменатель на множители:

2x^2+15x+25=0
D=225-200=25
[x=(-15+5)/4=-10/4=-2.5
[x=(-15-5)/4=-20/4=-5
2x^2+15x+25=2(x+2.5)(x+5)

5-4x-x^2=0
x^2+4x-5=0
[x=1
[x=-5
5-4x-x^2=-(x-1)(x+5) 

limx->-5 (2x^2+15x+25)/(5-4x-x^2) = limx->-5 (2(x+2.5)(x+5)/-(x-1)(x+5)) = limx->-5 (2(x+2.5)/(1-x)) = 2(-5+2.5)/(1+5) = 2*(-2.5)/6 = -5/6