Question

两个分式计算,一个分式解方程,计算：（1）x²-9/x²+2x乘x²-4/x²-3x（2）x²-y²/x÷x²+2xy+

Answer 1

解计算

(1)原式=(x²-9)/(x²+2x) × (x²-4)/(x²-3x)

=(x+3)(x-3)/[x(x+2)] × (x+2)(x-2)/[x(x-3)] 约分

=(x+3)/x × (x-2)/x

=(x+3)(x-2)/x²

(2)原式=(x²-y²)/x ÷ (x²+2xy+y²)/x²

=(x+y)(x-y)/x × x²/(x+y)² 约分

=(x-y) × x/(x+y)

=x(x-y)/(x+y)

解方程：1/(x-1)=1/(x²-1)

方程两边同时乘最简公分母(x²-1)

x+1=1

x=0

检验：把x=0代入最简公分母

x²-1=0-1=-1≠0

x=0是原方程的根