Question

化簡(jiǎn)

x2+1

x2-1

-

x-2

x-1

÷

x-2

2

，并用你喜歡的一個(gè)x的值求代數(shù)式的值．

Answer 1

分析：首先把除法運(yùn)算轉(zhuǎn)化成乘法運(yùn)算，進(jìn)行約分，然后進(jìn)行減法運(yùn)算，進(jìn)行通分化簡(jiǎn)，最后代值計(jì)算．

解答：解：原式=

x2+1

(x+1)(x-1)

-

x-2

x-1

•

x

x-2

=

x2+1

(x+1)(x-1)

-

x

x-1

=

x2+1

(x+1)(x-1)

-

x(x+1)

(x+1)(x-1)

=

x2+1-x2-x

(x+1)(x-1)

=

1-x

(x+1)(x-1)

=-

1

x+1

；
當(dāng)x=5時(shí)，原式=-

1

x+1

=-

1

5+1

=-

1

6

．

點(diǎn)評(píng)：本題主要考查分式的化簡(jiǎn)求值，把分式化到最簡(jiǎn)是解題的關(guān)鍵．