Question

First we increased the denominator of a positive fraction by 3 and then we decreased it by 5. the sum of the resulting fractions proves to be equal to 2/3. find the denominator of the fraction if its numerator is 2.

Answer 1

let the denominator of the fraction be x.
so the required fraction equals to 2/x
if we increase the denominator by 3 then the fraction would be 2/3+x.--equation 1st
if we decrease 5 from the from the equation 1 =2/3+x-5
2/x-2----equation2nd
we know that the addition of these equations is 2/3
according to the question

2/3+x+2/x-2 = 2/3

2(x-2) + 2(3+x)/(3+x)(x-2)=2/3

2x-4 + 6 + 6x/ 3x-6+x^2- 2x=2/3

8x-2/x-6+x^2=2/3

( 8x-2)×3/(x-6+x^2=0

24x-6/3x-18+3x^2=0

24x-6=3x-18 + 3x^2

25x-3x=18+6+3x^2

22x=24+3x^2

22

wil trll you rest of the answer later . keep patience