Answer :
Answer:
Step-by-step explanation:Let the denominator of the original fraction be \( x \).
According to the problem, the numerator is \( x - 2 \).
The original fraction can then be expressed as:
\[
\frac{x - 2}{x}
\]
When one is added to the denominator \( x \), the new fraction becomes \( \frac{1}{2} \). Therefore, the new fraction is:
\[
\frac{x - 2}{x + 1} = \frac{1}{2}
\]
To eliminate the fraction, cross-multiply:
\[
2(x - 2) = x + 1
\]
Expand and solve the equation:
\[
2x - 4 = x + 1
\]
Subtract \( x \) from both sides:
\[
x - 4 = 1
\]
Add \( 4 \) to both sides to solve for \( x \):
\[
x = 5
\]
So, the denominator of the original fraction is \( x = 5 \).
Now, find the numerator using \( x - 2 \):
\[
x - 2 = 5 - 2 = 3
\]
Therefore, the original fraction is:
\[
\frac{3}{5}
\]
To verify:
1. Check the condition: The numerator \( 3 \) is indeed \( 2 \) less than the denominator \( 5 \).
2. When \( 1 \) is added to the denominator \( 5 \), the new fraction becomes \( \frac{3}{6} \), which simplifies to \( \frac{1}{2} \).
Hence, everything checks out, and the original fraction is \( \boxed{\frac{3}{5}} \).