3. The numerator of a fractwilles, the age of the son, find the presen

1.	3. The numerator of a fractwilles, the age of the son, find the present age 1numerator of a fraction is one less than the denominaTf 3 is added to each of thenumerator and denominator, the fraction is increased byFind the fraction.28
Answer» Let denominator of fraction be x then numerator = x - 1 As per given condition(x - 1 + 3)/(x + 3) =(x - 1)/x + 3/28 (x + 2)/(x + 3) - (x-1)/x = 3/28 28[(x + 2)x - (x + 3)(x - 1)]= 3x(x + 3) 28(x^2 + 2x - x^2 + x - 3x +3)= 3x^2 + 9x 3x^2 + 9x - 84 = 0 3x^2 + 21x - 12x - 84 = 0 3x(x + 7) - 12(x + 7) = 0 (3x - 12)(x + 7) = 0 x = 4, - 7 Therefore, For x = 4, fraction = 3/4For x = - 7 fraction = - 8/-7 3/4, -8/-7

3. The numerator of a fractwilles, the age of the son, find the present age 1numerator of a fraction is one less than the denominaTf 3 is added to each of thenumerator and denominator, the fraction is increased byFind the fraction.28

Answer»

Let denominator of fraction be x then numerator = x - 1

As per given condition(x - 1 + 3)/(x + 3) =(x - 1)/x + 3/28

(x + 2)/(x + 3) - (x-1)/x = 3/28

28[(x + 2)x - (x + 3)(x - 1)]= 3x(x + 3)

28(x^2 + 2x - x^2 + x - 3x +3)= 3x^2 + 9x

3x^2 + 9x - 84 = 0

3x^2 + 21x - 12x - 84 = 0

3x(x + 7) - 12(x + 7) = 0

(3x - 12)(x + 7) = 0

x = 4, - 7

Therefore, For x = 4, fraction = 3/4For x = - 7 fraction = - 8/-7

3/4, -8/-7