两个分式计算,一个分式解方程,
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/04 23:47:12
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+y²/x²
解方程:
(1)1/x-1=1/x²-1
计算:
(1)x²-9/x²+2x乘x²-4/x²-3x
(2)x²-y²/x÷x²+2xy+y²/x²
解方程:
(1)1/x-1=1/x²-1
![两个分式计算,一个分式解方程,](/uploads/image/z/17483873-41-3.jpg?t=%E4%B8%A4%E4%B8%AA%E5%88%86%E5%BC%8F%E8%AE%A1%E7%AE%97%2C%E4%B8%80%E4%B8%AA%E5%88%86%E5%BC%8F%E8%A7%A3%E6%96%B9%E7%A8%8B%2C)
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
(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