A denominator of a fraction exceeds the numerator by 1 if 2 is taken from each the sum of the reciprocal of the new fraction and 4 times the original fraction is 5. Find the original fraction

Answer 1

original fraction ---- x/(x+1)

new fraction = (x-2)/(x-1)

(x-1)/(x-2) + 4x/(x+1) = 5
times (x-2)(x+1), the LCD

(x-1)(x+1) + 4x(x-2) = 5(x-2)(x+1)
x^2 - 1 + 4x^2 - 8x = 5x^2 - 5x - 10
3x - 9 = 0
x = 3

original fraction is 3/4

check:
new fraction = 1/2
1/(1/2) + 4(3/4)
= 2 + 3 = 5 , as needed