The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2,
the fraction is increased by . Find the original fraction.

There is missing data in the problem, I have added it to solve the problem. You can use your real data once you understand the explanation.

Original fraction:

Step-by-step explanation:

The numerator of a fraction is 1 less than the denominator and when both parts are increased by 2, the value of the fraction increases by 1/24. Find the original fraction.

Let's call:

x=original numerator

x+1=original denominator

x+2=increased numerator

x+3=increased denominator

Original fraction:

Increased fraction:

The difference between both is 1/24:

Multiply by (x+3)(x+1):

Simplifying each fraction when possible:

Operating:

Simplifying:

Multiplying by 24:

Rearranging:

Factoring:

We have two solutions:

Selecting the first solution:

Original fraction:

Increased fraction:

The difference between both is:

This is a valid solution

Selecting the second solution:

Original fraction:

Increased fraction:

The difference between both is:

This solution is only valid if we express the fractions with their negative values. When we simplify them, the first condition is not met. Thus, the solutions are:

Original fraction:

Note: The last solution can be arguable because the real simplified fraction is not a solution. My opinion is that it's valid as long as it's expressed with their original signs.

by definition, an arc subtended by a central angle of some given measure has the same measure. so .