Question

一道数学题，要过程，要详细

已知1/a+1/b=1/a+b,则b/a+a/b的值是多少？我知道等于-1请告诉我过程，拜托了

Answer 1

1/a+1/b=1/a+b
通分得:(a+b)/ab=1/(a+b)
(a+b)^2=ab
展开得：a^2+b^2=-ab
两边同时除以ab即：b/a+a/b=-1

Answer 2

原式可化为 (a+b)/ab=1/a+b
即 a^2+b^2=-ab
等式两边同时处以 ab，得、
a/b+b/a=-1

Answer 3

1/a+1/b=1/a+b,
(a+b)/ab=1/(a+b)
(a+b)^2=ab
b/a+a/b
=（a^2+b^2)/ab
={(a+b)^2-2ab}/ab
=-ab/ab
=-1

Answer 4

1/a+1/b=1/a+b,
(a+b)/a+(a+b)/b=1,
1+b/a+1+a/b=1
b/a+a/b+2=1
b/a+a/b=-1

Answer 5

-1
1/a+1/b=1/a+b
两面同乘以a+b
1+b/a+1+a/b=1
b/a+a/b=-1