P (x) a0xm + a1xm-1 + · · · + am-1x + am
f(x) = = ,
Q(x) b0xn + b1xn-1 + · · · + bn-1x + bn
a0 = 0 b0 = 0
8 8
m e" n P (x) Q(x)
f
m < n P (x) Q(x) f
x2 2x4-3x+5
f(x) = g(x) =
x2-1 x-3
x2+2x-10 x+2
h(x) = k(x) =
x3-2x2+1 5x5+4x+7
P (x) Q(x)
x4 x2(x2 + 1) - 1(x2 + 1) + 1 1
f(x) = = = x2 - 1 +
x2 + 1 x2 + 1 x2 + 1
A Bx+C
(x-a)K (x2+bx+c)l
" = b2 - 4c < 0 A B C a b c k l
P (x)
Q(x)
Q(x) x - a
" < 0
P (x)
Q(x)
(x - a)k Q(x)
A1 A2 Ak
+ + · · · + ,
x - a (x - a)2 (x - a)k
(x2 + bx + c)l Q(x)
B1x + C1 B2x + C2 Blx + Cl
+ + · · · + .
x2 + bx + c (x2 + bx + c)2 (x2 + bx + c)l
A1, A2, . . . , Ak, B1, . . . , Bl, C1, . . . , Cl