ANSWER: 3/12 is the original fraction.
Let the denominator be x
the numerator be x - 9 (nine less than the denominator)
If 3 is added to the numerator, the new fraction is 1/2
[tex] \frac{(x-9)+3}{x} = \frac{1}{2} [/tex]
[tex] \frac{x-6}{x} = \frac{1}{2} [/tex]
LCD (Least common denominator is (2)(x)
[tex](2)(x) \frac{(x-6)}{x} = \frac{1}{2} (2)(x)[/tex]
2x - 12 = x
2x - x = 12
x = 12
The original fraction: (Substitute 12 for x)
x-9
x
12-9
12
3/12 Original fraction.
To check when 3 is added to numerator, the new fraction is 1/2:
3 + 3 = 1/2
12
6/12 = 1/2
1/2 = 1/2
