Question

The numerator of a fraction is one less than its denominator. If three is added to each of the numerator and denominator, then the fraction is increased by $\frac{2}{28}$ . Find the fraction.
OR
The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

Answer 1

Answer:

Step-by-step explanation:

if x/y represents the fraction then

x + 1 = y.

om the other hand

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

(x + 3)/(x + 4) = x/(x + 1) + 1/14

1 - 1/(x + 4) = 1 - 1/(x + 1) + 1/14

1/(x + 1) - 1/(x + 4) = 1/14

3/(x + 1)(x + 4) = 1/14

(x + 1)(x + 4) = 42

x^2 + 5*x - 38 = 0

x = (-5 + sqrt(177))/2

x/y = x/(x + 1) = (81 - sqrt(177))/84.