#### Question

In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by. Find the fraction.

#### Solution

Let the fraction be `x/(x + 3)`

When 1 is subtracted from both numerator and denominator, then the fraction be comes `(x - 1)/(x + 2)`

From the given information we have

`x/(x + 3) - 1/14 = (x - 1)/(x + 2) `

`(14x - x - 3)/(14(x + 3)) = (x - 1)/(x + 2)`

`(13x +- 3)/(14(x + 3)) = (x - 1)/(x + 2)`

`(13x - 3)(x + 2) = 14(x^2 + 28x - 42)`

`x^2 + 5x - 36 = 0`

`x^2 + 9x - 4x - 36 = 0`

x(x + 9)(x - 4) = 0

(x + 9)(x - 4) = 0

x = -9, 4

Since x cannot be negative So x = 4

Hence the fraction is `x/(x + 3) = 4/7`

Is there an error in this question or solution?

Solution In a Certain Positive Fraction, the Denominator is Greater than the Numerator by 3. If 1 is Subtracted from the Numerator and the Denominator Both, the Fraction Reduces By. Find the Fraction. Concept: Quadratic Equations.