In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2/3. Find the original fraction.

And please solve it only by using one variable.

If We Suppose that 3 is added to both

Let The Denominator Be x

2*numerator= x+2

numerator = x+2 / 2

Fraction = x+2 / 2*1/x = x+2/2x

New Numerator = x+2/2+3 = x+8/2

New Denominator = x+3

New Fraction = x+8/2*1/x+3 = x+8/2x+6

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

3x+24 = 4x+12

x = 12

Numerator = x+2 / 2 = 12+2/2 = 7

Hence Fraction = 7/12