分式的加减 1.下列计算正确吗?不正确,请改正。 (1)x分之x-1+x分之2...
发布网友
发布时间：2024-05-15 14:28
共2个回答
热心网友
时间：2024-06-03 16:59
错误，原式=(x+1)/x
（2）(x+y)/x-y/x=1
正确
（3）1/x+1/(-x)=0
正确
（4）x/(x-1)+1/(1-x)=(x+1)/(x-1)
错误，原式=x/(x-1)-1/(x-1)=(x-1)/(x-1)=1
2.（1）2/m+1/m
=3/m
（2）3b/(xy)-b/(xy)
=(3b-b)/(xy)
=2b/(xy)
（3）a/(a+b)+b/(a+b)
=1
（4）5x/(2x-y)-(x+2y)/(2x-y)
=(4x-2y)/(2x-y)
=2
（5）2/(-mn)+10/mn
=8/mn
（6）(t+4k)/(9k²-4t²)+(k-t)/(4t²-9k²)
=(t+4k)/(9k²-4t²)-(k-t)/(9k²-4t²)
=(3k+2t)/(9k²-4t²)
=(3k+2t)/[(3k+2t)(3k-2t)]
=1/(3k-2t)
3.（1）2y/(x+y)+(x-y)/(x+y)
=(x+y)/(x+y)
=1
（2）2m/(m-n)²-2n/(n-m)²
=2(m-n)/(m-n)²
=2/(m-n)
（3）M=2xy/(x²-y²)
N=(x²+y²)/(x²-y²)
∴M+N=(x+y)²/(x+y)(x-y)
=(x+y)/(x-y)
M-N=-(x-y)²/(x+y)(x-y)
=(y-x)/(x+y)
N-M=(x-y)²/(x+y)(x-y)
=(x-y)/(x+y)
当x=2y时
M+N=3
M-N=-1/3
N-M=1/3
热心网友
时间：2024-06-03 17:01
错误，原式=(x+1)/x
（2）(x+y)/x-y/x=1
正确
（3）1/x+1/(-x)=0
正确
（4）x/(x-1)+1/(1-x)=(x+1)/(x-1)
错误，原式=x/(x-1)-1/(x-1)=(x-1)/(x-1)=1
2.（1）2/m+1/m
=3/m
（2）3b/(xy)-b/(xy)
=(3b-b)/(xy)
=2b/(xy)
（3）a/(a+b)+b/(a+b)
=1
（4）5x/(2x-y)-(x+2y)/(2x-y)
=(4x-2y)/(2x-y)
=2
（5）2/(-mn)+10/mn
=8/mn
（6）(t+4k)/(9k²-4t²)+(k-t)/(4t²-9k²)
=(t+4k)/(9k²-4t²)-(k-t)/(9k²-4t²)
=(3k+2t)/(9k²-4t²)
=(3k+2t)/[(3k+2t)(3k-2t)]
=1/(3k-2t)
3.（1）2y/(x+y)+(x-y)/(x+y)
=(x+y)/(x+y)
=1
（2）2m/(m-n)²-2n/(n-m)²
=2(m-n)/(m-n)²
=2/(m-n)
（3）M=2xy/(x²-y²)
N=(x²+y²)/(x²-y²)
∴M+N=(x+y)²/(x+y)(x-y)
=(x+y)/(x-y)
M-N=-(x-y)²/(x+y)(x-y)
=(y-x)/(x+y)
N-M=(x-y)²/(x+y)(x-y)
=(x-y)/(x+y)
当x=2y时
M+N=3
M-N=-1/3
N-M=1/3
