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Answer 1 · 2017-10-28T07:16:07

Let the numerator of the number be #x#
As the denominator of a fraction is one more than twice the numerator, we have denominator #=2x+1#

Hence the fraction is # x/(2x+1)=y (say)#, we can write

Given that the sum of fraction and its reciprocal is 58/21

# y+1/y=58/21#

#=>21y^2-58y+21=0#

#=>21y^2-49y-9y+21=0#

#=>7y(3y-7)-3(3y-7)=0#

#=>(3y-7)(7y-3)=0#

so #y=7/3 or 3/7#

Taking fraction to be proper as #x<2x+1 #we can write

# x/(2x+1)=y =3/7#

#=>7x=6x+3#

So #x=3#

Hence numerator is #3# and denominator is #7#

So the number is #3/7#