the denominator is one more than  twice  the numerator , if the sum of the fraction and  its recoprocal is 2  16/21 . find the fraction

let the numerator be 'x' then denominator is'2x+1'

given="x / 2x+1" + "2x+1/x"=2 16/21

then="x / 2x+1" + "2x+1/x"=58/21

=x(x)+2x+1(2x+1) / 2x+1(x=58/21

=x²+(2x+1)²  / 2x²+x=58/21

=x²+4x²+4x+1 / 2x²+x=58/21

=5x² +4x+1 / 2x²+x=58/21

=5x² +4x+1(21)=58(2x²+x)

=105x² +84x+21=116x² +58x

=116x² +58x-105x² -84x-21=0

=11x² - 26x-21=0

by solving using x= -(b)+rootb² -4ac /2a

we get x=3 so the fraction is 3/7

check

3/7 +7/3 =49 +9 /21=58 /21

hence verified