A fraction has a denominator that is one less than twice its numerator. When both the numerator and denominator are increased by 1, the fraction equals 3/5. What is the original fraction?

Explanation

Let the numerator be n and the denominator be d. Given that d = 2n - 1. After increasing both by 1, the fraction becomes (n + 1)/(d + 1) = 3/5. Cross-multiplying gives 5(n + 1) = 3(d + 1), which simplifies to 5n + 5 = 3(2n - 1) + 3. Solving for n yields n = 5. Substituting back, d = 2(5) - 1 = 9. Therefore, the original fraction is 5/9.