The sum of reciprocals of rehman’s ages 3 years ago and 5 years from now is 1/3. find his present age

His age is 7 years.

Step-by-step explanation:

Let Rehman's  present age be x years.

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

Multiply through by the LCD 3(x - 3)(x + 5):

3(x + 5) + 3(x - 3) = (x + 5)(x - 3)

3x + 15 + 3x - 9 = x^2 + 2x - 15

x^2 + 2x - 6x - 30 + 9 = 0

x^2 - 4x - 21 = 0

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

x = 7  (answer).

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.