a numerator is a fraction one less than the denominator.if 3 is added to both the numerator and denominator the fraction increase to 3/28
Answers
Answer:
Let the denominator be x.
A.T.Q., the numerator will be (x - 1).
Original fraction = (x-1)/x
Now, as given in the question, 3 is added to both numerator and denominator.
So,
Numerator = x - 1 + 3 = x + 2
Denominator = x + 3
A.T.Q.
On further solving, we get
Cross - multiplication.
28x(x + 2) = (x + 3)(31x - 28)
28x(x + 2) = x(31x - 28) + 3(31x - 28)
28x² + 56x = 31x² - 28x + 93x - 84
28x² + 56x = 31x² + 65x - 84
Transposing the terms.
28x² - 31x² = 65x - 56x - 84
- 3x² = 9x - 84
3x² + 9x - 84 = 0
3(x² + 3x - 28) = 0
x² + 3x - 28 = 0
Using Middle Term Factorisation, we get
x² - 4x + 7x - 28 = 0
x(x - 4) + 7(x - 4) = 0
(x + 7)(x - 4) = 0
Using zero product rule, we get
x + 7 = 0 and x - 4 = 0
x = - 7 and x = 4
Here, x is a natural number, where x > 0.
Hence, x = 4
The required fraction is : 3/4