化簡數學式的問題

1.
xy-x-y
把 x 找出來 xy-x-y = x(y-1) 你就知道原來含 y 的因式是 y-1
把 y 找出來 xy-x-y = y(x-1) 你就知道原來含 x 的因式是 x-1
相乘 (x-1)(y-1)= xy-x-y+1
所以 0< xy-x-y<5
=>　 1< xy-x-y+1 <6
=>　 1< (x-1)(y-1) <6

2.
類似上則的作法
3ab-4a-5b = a(3b-4) -5b
3ab-4a-5b = b(3a-5) -4a
找到因式是 3a-5 與 3b-4
則 (3a-5)(3b-4) = 3ab-4a-5b+20 = -(5b+4a-3ab)+20 = 20

2015-07-05 12:06:15 補充：
xy-x-y = x(y-1) -y
xy-x-y = y(x-1) -x
漏了一下，抱歉！

1. 0< xy-x-y<5
==>0<5
==>1+0<5+1

湊y-1的因式把多的減掉
兩邊平衡都加1
==>1<(x-1)(y-1)<6


2. 5b+4a-3ab=0
==>3ab-4a-5b=0
==>a(3b-4)-(5/3)*(3b-4)-(20/3)=0

湊3b-4的因式把多的減掉
兩邊平衡

==>(a-(5/3))(3b-4)=20/3
==>(3a-5)(3b-4)=20

2015-07-05 14:11:03 補充：
1.漏字補充
0< xy-x-y<5
==>0小於x(y-1)-y小於5
==>1+0小於x(y-1)-(y-1)小於5+1
==>1小於(x-1)(y-1)小於6

1. 0< xy-x-y<5 要怎化簡成1<(x-1)(y-1)<6
Sol
0<5
0<5
0<5
1<6
1<(x-1)(y-1)<6