Question

求极限lim X→3，X²-2X-3分之X²-8X+15的运算过程

Answer 1

解:将分子分母分别因式分解,既得:(x-3)(x-5)/(x+1)(x-3) 上下一同约去公因式(x-3)
得lim(x→3) (x-5)/(x+1)
再将x=3 代入.即刻求得其极限值为- (1/2)

Answer 2

X²-8X+15=(x-3)(x-5)
X²-2X-3=(x-3)(x+1)
可把(x-3)约去
lim X→3,(X²-8X+15)/(X²-2X-3)
=lim X→3,(x-5)/(x+1)
=(3-5)/(3+1)
=-1/2

Answer 3

(x^2 - 8 x + 15)/(x^2- 2 x - 3\)
=(x-5)(x-3)/(x+1)(x-3)
=x-5/x+1
原式=lim X→3{(x-5)/(x+1)}
=(3-5)/(3+1)
=-1/2

Answer 4

X²-8X+15/X²-2X-3
lim X→3=(x-3)(x-5)/(x-3)(x+1)
(x-3)约掉
(x-5)/(x+1)带入lim X→3
=-1/2

Answer 5

（X²-8X+15）/（X²-2X-3）=（x-3）(x-5)/(x-3)(x+1)=(x-5)/(x+1)
所以X→3，(x-5)/(x+1)→-1/2
极限为-1/2