The denominator of a fraction is 1 less than twice the numerator. if the numerator and denominator are both increased by 1, the fraction becomes 3/5. find the fraction?

Mathematics
1

the denominator of a fraction is 1 less than twice the numerator. if the numerator and denominator are both increased by 1, the fraction becomes 3/5. find the fraction?

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Answer:

Let’s begin by defining the numerator of the fraction as x. Then, we know that the denominator is 1 less than twice the numerator, or 2x - 1.

So, the original fraction can be expressed as x / (2x - 1).

We also know that if both the numerator and denominator are increased by 1, the fraction becomes 3/5. That means we can create the equation:

(x+1) / (2x) = 3/5

We can solve for x by cross-multiplying and simplifying:

5(x+1) = 3(2x)

5x + 5 = 6x

5 = x

Now that we have found the value of x, we can substitute it into the original expression for the fraction:

x / (2x - 1) = 5 / 9

Therefore, the fraction is \Large \frac{5}{9}.