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**

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