Math
posted by Anjana
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

Reiny
original fraction  x/(x+1)
new fraction = (x2)/(x1)
(x1)/(x2) + 4x/(x+1) = 5
times (x2)(x+1), the LCD
(x1)(x+1) + 4x(x2) = 5(x2)(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
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