已知a、b、c为实数,且ab/a+b=1/3,bc/b+c=1/4,ca/c+a=1/5.求abc/ab+bc+ca的值
问题描述:
已知a、b、c为实数,且
=ab a+b
,1 3
=bc b+c
,1 4
=ca c+a
.求1 5
的值 abc ab+bc+ca
答
将已知三个分式分别取倒数得:
=3,a+b ab
=4,b+c bc
=5,c+a ca
即
+1 a
=3,1 b
+1 b
=4,1 c
+1 c
=5,1 a
将三式相加得;
+1 a
+1 b
=6,1 c
通分得:
=6,ab+bc+ca abc
即
=abc ab+bc+ca
.1 6