Question

the denominator of a fraction is two more than its numerator. if the sum of the fraction and it's reciprocal is 34/15 find the fraction​

Answer 1

Answer:-

Let the numerator be x and denominator be x+2.

Required fraction = x/x+2

According to the question,

x/x+2 + x+2/x = 34/15

x^2 + (x+2)^2/x^2 + 2x = 34/15

x^2 + x^2 + 4x + 4/x^2 + 2x = 34/15

(2x^2 + 4x + 4)×15 = 34×(x^2 + 2x)

30x^2 + 60x + 60 = 34x^2 + 68x

34x^2 + 68x - 30x^2 - 60x - 60 = 0

4x^2 + 8x - 60 = 0

x^2 + 2x - 15 = 0

x^2 + 5x - 3x - 15 = 0

x (x + 5) - 3 (x + 5) = 0

(x + 5) + (x - 3) = 0

So, x + 5 = 0 or x - 3 = 0

x = -5 or x = 3

For x = -5,

x/x + 2 = 5/3

For x = 3,

x/x + 2 = 3/5