Question
Given ab=1 , a≠ -1 , b≠ -1 , find the value of \dfrac{1}{1+a}+\dfrac{1}{1+b}
Given ab=1 , a≠ -1 , b≠ -1 , find the value of \dfrac{1}{1+a}+\dfrac{1}{1+b}
\dfrac{1}{1+a}+\dfrac{1}{1+b}
=\dfrac{1+b+1+a}{(1+a)(1+b)}
=\dfrac{2+a+b}{1+a+b+ab}
=\dfrac{2+a+b}{1+a+b+1}
=1