Question

Algebraic structure problem:

Answer 1

LeT it be G=(-1,1) with x,y from G;
Show that:
\[\frac{ x+y }{ 1+xy } \epsilon G\]

Answer 2

@ganeshie8 @iPwnBunnies @phi @mathslover @nincompoop

Answer 3

For x= y = -1
\[\frac{ x+y }{ 1+xy} = -1 \in G\]
For x= y = 1
\[\frac{ x+y }{ 1+xy} = 1 \in G\]
For x= 1, y = -1
\[\frac{ x+y }{ 1+xy} = 0 \in G\]
Since it is true for extremes, so
\[\frac{ x+y }{ 1+xy}\in G\] for x,y in (-1,1)