numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the de

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numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denominator the new fraction is 2/3. find the fraction.

Let n be the numerator.
Let d be the denominator.

We're given 2 equations:

1. n = d - 5
2. (n + 1)/(d + 1) = 2/3

Substitute equation (1) into equation (2) for n:
(d - 5 + 1) / (d + 1) = 2/3
(d - 4) / (d + 1) = 2/3

Cross multiply:
3(d - 4) = 2(d + 1)

To solve this equation for d, we type it in our search engine and we get:
d = 14

Substitute d = 14 into equation (1) to solve for n:
n = 14 - 5
n = 9

Therefore, our fraction n/d is:
9/14