Problema Solution
In an unknown fraction thedenominator is 1 more than twice the numerator.when 2/1/10 is added to the unknown fraction,yhe result is equal to the reciprocal of the unknown fractio.find the unknown fraction.
Answer provided by our tutors
Let the numerator be x
the denominator will be 2x + 1
the fraction will be x/2x + 1
As per question. x/2x+1 + 21/10 = 2x+1/x
solving this we get,
(52x+21)/20x+10)= (2x+1)/x
52x^2+21x= 40x^2+20x+20x+10
12x^2-19x-10= 0
solving using middle term splitting
12x^2-24x+5x-10 = 0
12x(x-2)+5 (x-2 ) =0
(x-2) (12x + 5) = 0
Hence we get numerator that is x = 2 and the denominator will be 2*2+1 = 5
Therefore, the fraction is, 2/5.