Question

The denominator of a fraction exceeded the numerator by 1. If 2 be taken from each, the sum of the reciprocal of the new fraction and 4 times the original fraction is five. Find the original fraction

Answer 1

Step-by-step explanation:

iinitially let x be the numerator, so (x+1) will be the denominator. so the fraction is (x)/(x+1).

{(x+1-2)/(x-2)} + 4*{(x)/(x+1)} = 5

{(x-1)/(x-2)} + 4x/ (x+1) = 5

(x^2) -1+ (4x^2) - 8x = 5 (x+1) ( x-2)

5x^2 - 8x -1 = {(5x^2)- 10x + 5x -10}

3x = 9

x = 3

therefore original fraction is (x)/(x+1)

= (3/4)