Question

先化簡(jiǎn)代數(shù)式

x-1

x+2

÷

x2-1

x3+4x+4x

-

2x+1

x+1

，再選一個(gè)你喜歡的數(shù)作為x的值代入求值．（溫馨提示：注意要使所給的代數(shù)式有意義喲�。�

Answer 1

x-1

x+2

÷

x2-1

x3+4x2+4x

-

2x+1

x+1

=

x-1

x+2

×

x(x+2)2

(x+1)(x-1)

-

2x+1

x+1

=

x2+2x

x+1

-

2x+1

x+1

=

x2+2x-2x-1

x+1

=

x2-1

x+1

=

(x+1)(x-1)

x+1

=x-1，
∵分式必須有意義，
∴x+2≠0，x³+4x²+4x≠0，x²-1≠0，x+1≠0，
解得x≠-2，x≠0，x≠±1，
∴取x=2時(shí)，原式=x-1=2-1=1．