Question

若a，b，c是非零實數，求

a

b+c

=

b

a+c

=

c

a+b

的值．

Answer 1

①當a+b+c=0時，a+b=-c，于是

a

b+c

=

b

a+c

=

c

a+b

=

c

-c

=-1，
②當a+b+c≠0時，由等比性質有

a

b+c

=

b

a+c

=

c

a+b

=

a+b+c

b+c+a+c+a+b

=

1

2

綜合①、②有

a

b+c

=

b

a+c

=

c

a+b

的值為-1或

1

2

．