解一题:
原式=[1/(m²-49)]÷[m/(m²-7m)]
={1/[(m-7)(m+7)]}÷{m/[m(m-7)]}
={1/[(m-7)(m+7)]}×(m-7)
=1/(m+7)
解二题:
原式=b/(a²+ab)+1/(a+b)
={b/[a(a+b)]}+{a/[a(a+b)]}
=(a+b)/[a(a+b)]
=1/a
=1/1
=1
解三题:
x/(x-1) -1=1/[(x+1)(x-1)] 方程两边同时乘最简公分母(x+1)(x-1)
x(x+1)-(x+1)(x-1)=1
x²+x-x²+1=1
x=0
检验:
把x=0代入(x+1)(x-1)=(0+1)×(0-1)=-1≠0
所以,x=0是原方程的根