Question

八下 分式的基本性质

通分
（10a-b/-a²，a+b/3a：(2) 5/-4ab²，4/5a²b (3)x/a(x-y),y/b(y-x) (4)a/(y-x)²,b/(x-y)(x+y) 4.①3-2b,2a/b-a ②1/a+1,3/1-a，5/a²-1 ③a/a-b，b/a²-b²，c/a+b； ④a/a²-4，a-1/a-2，a+2/a²-4a+4

Answer 1

（1）10a-b/-a²，a+b/3a：
10a-b/-a²=(b-10a)/a²=(3b-30a)/3a²
a+b/3a=（a²+ab)/3a²
（2） 5/-4ab²，4/5a²b
5/-4ab²=-25/20a²b²
4/5a²b=16/20a²b²
（3）x/a(x-y)，y/b(y-x)
x/a(x-y)=bx/ab(x-y)
y/b(y-x)=-y/b(x-y)=-ay/ab(x-y)
（4）a/(y-x)²，b/(x-y)(x+y)
a/(y-x)²=a(x+y)/(x+y)(x-y)²
b/(x-y)(x+y)=b(x-y)/(x+y)(x-y)²

4.
①3-2b，2a/b-a
3-2b=(3-2b)(b-a)/(b-a)
2a/b-a=2a/(b-a)
②1/a+1，3/1-a，5/a²-1
1/a+1=(a-1)/（a²-1）
3/1-a=-3/(a-1)= -3(a+1)/(a²-1)
5/a²-1 =5/(a²-1)
③a/a-b，b/a²-b²，c/a+b
a/a-b=a(a+b)/(a²-b²)
b/a²-b²=b/(a²-b²)
c/a+b=c(a-b)/(a²-b²)
④a/a²-4，a-1/a-2，a+2/a²-4a+4
a/a²-4=a(a-2)/(a-2)²(a+2)
a-1/a-2=(a-1)(a-2)(a+2)/(a-2)²(a+2)
a+2/a²-4a+4=(a+2)²/(a-2)²(a+2)