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
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