Question

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

Steven Zheng Steven Zheng posted 1 week ago


Answer

\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

Steven Zheng Steven Zheng posted 1 week ago

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