數學問題(給60點)!!!!!!!

1. (a) 2x-2y = 2*(x-y)
8y+4x = 2*2*(2y+x)
LCM = 2*2*(x-y)*(2y+x) = 4(x-y)(2y+x)
(b) 2xy+x^2 = x*(2y+x)
3x^2-3xy = 3*x*(x-y)
LCM = 3x(2y+x)(x-y)
(c) [1/(2x-2y)-1/(8y+4x)]除以[2/(2xy+x^2)+3/(3x^2-3xy)]
= {2(2y+x) / [4(x-y)(2y+x)] - (x-y) / [4(x-y)(2y+x)]} 除以 {2*3(x-y)/[3x(2y+x)(x-y)] + 3(2y+x)/[3x(2y+x)(x-y)]}
= (4y+2x-x+y) / [4(x-y)(2y+x)] 除以 9x/[3x(2y+x)(x-y)]
= (5y+x) / 4 除以 3
= (5y+x)/12
2. [(xy-x^2)/x^2y(x+y)]除以(x^2-xy)/x^2y+8/(x-y)
= [x(y-x)/x^2y(x+y)] 除以[x(x-y)/x^2y + 8/(x-y)]
= [(y-x)/xy(x+y)] 除以 [(x-y)/xy + 8/(x-y)]
= [(y-x)/xy(x+y)] 除以 [(x-y)(x-y)/xy(x-y) + 8xy/xy(x-y)]
= [(y-x)/xy(x+y)] 除以 [(x^2-2xy+y^2+8xy)/xy(x-y)]
= [(y-x)/(x+y)] 除以 [(x^2+6xy+y^2)/(x-y)]
= [(y-x)/(x+y)] * [(x-y)/(x^2+6xy+y^2)]
= -(x-y)^2/[(x+y)(x^2+6xy+y^2)]
3.(a) 3x/(y-x)^2-2/(x-y)
= 3x/(x-y)^2 - 2(x-y)/(x-y)^2
= (3x-2x+2y)/(x-y)^2
= (x+2y)/(x-y)^2
(b) 3y/(x-y)^2-1/(y-x)
= 3y/(x-y)^2 + (x-y)/(x-y)^2
= (3y+x-y)/(x-y)^2
= (x+2y)/(x-y)^2
(c) [3x/(y-x)^2-2/(x-y)]除以[3y/(x-y)^2-1/(y-x)]
= [(x+2y)/(x-y)^2] 除以 [(x+2y)/(x-y)^2]
= 1
4. (a) (p-q)^2= (p-q) * (p-q) = (q-p) * (q-p)
(q-p)^3= (q-p) * (q-p) * (q-p)
LCM = (q-p)^3
(b) [1/(p-q)^2-(p+q)/(q-p)^3]乘以(q-p)^2/(2p+q)
= [(q-p)/(q-p)^3 - (p+q)/(q-p)^3] * [(q-p)^2/(2p+q)]
= [(q-p-p-q)/(q-p)^3] * [(q-p)^2/(2p+q)]
= -2p/(q-p)^3] * [(q-p)^2/(2p+q)]
= -2p/(q-p)*[1/(2p+q)]
= 2p/[(p-q)(2p+q)]

2010-01-10 11:48:17 補充：
那裏錯了,讓我看過清楚.

第1題和第二題及第四題
錯了一些不可錯的東西