Let the denominator of the fraction be x. Then the numerator can be represented as x – 4.
The fraction can thus be expressed as:
Fraction = (x – 4) / x
According to the problem, if we add 1 to both the numerator and denominator, the fraction becomes 12:
((x – 4) + 1) / (x + 1) = 12
We can simplify the left side:
(x – 3) / (x + 1) = 12
Now, we cross-multiply to eliminate the fraction:
x – 3 = 12(x + 1)
Expanding this gives:
x – 3 = 12x + 12
Now we can rearrange the equation:
x – 12x = 12 + 3
-11x = 15
Dividing both sides by -11 gives:
x = -15/11
Now that we have x, we can find the numerator:
Numerator = x – 4 = (-15/11) – 4
To convert 4 into a fraction, we can express it as (44/11), which gives us:
Numerator = (-15/11) – (44/11) = -59/11
Thus, the fraction can be expressed as:
Fraction = (Numerator/Denominator) = (-59/11) / (-15/11)
Which simplifies to:
Fraction = 59/15
In conclusion, the fraction whose numerator is 4 less than the denominator and becomes 12 when adding 1 to both is 59/15.