the denominator of a fraction exceeds 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 5 . find the original fraction
Answers
Answered by
30
Reiny Wednesday, August 10, 2016 at 8:28am
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 ,
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 ,
Answered by
10
Answer:
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
Hope it helps u friend!!
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