# The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

The fraction is a part of a whole expressed as N/D.

## Answer: The required rational number is 13/21.

Let's find out the rational number with the given conditions.

**Explanation:**

Assume the numerator of the fraction as a variable.

- Use the first condition to express the denominator in the form of a variable
- Use the second condition to form the equation.

Let the numerator of the rational number be x.

Given that, the denominator of the rational number is 8 more than the numerator.

Then, denominator = (x + 8)

x / (x + 8) is the rational number.

Given that, (N + 17) / (D - 1) = 3/2

[(x) + 17] / [ (x + 8) - 1] = 3/2

[x + 17 ] / [ x + 7] = 3/2

By cross-multiplication, we get:

2(x + 17) = 3(x + 7)

2x + 34 = 3x + 21

34 - 21 = 3x - 2x

13 = x

Numerator of the rational number: x = 13

Denominator of the rational number: x + 8 = 13 + 8 = 21

Rational number = 13/21

### Thus, the required rational number is 13/21.

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