the denominator of a fraction in the simplest form is greater than the numerator by 1. if 4 is added to the numerator, and 3 is subtracted from the denominator, then the fraction itself is increased by 2 1/6. find the original fraction
+128456 Let the original fraction be x / ( x + 1)
So 2 1/6 = 13/6
So we have
x / (x + 1) + 13/6 = (x + 4) / (x - 2) simplify
(6x + 13 (x + 1) ) / (6 ( x + 1) ) = (x + 4) /( x - 2)
(19x + 13) ( x - 2) = 6( x + 1) ( x + 4)
19x^2 -25x - 26 = 6(x^2 + 5x + 4)
19x^2 - 25x - 26 = 6x^2 + 30x + 24
13x^2 - 55x - 50 = 0 factor as
(13x +10) ( x - 5) = 0
Since we probably want an integer answer....the second factor is what we need
x - 5 = 0
x = 5
The original fraction is x / (x + 1) = 5 / 6
Proof
5/6 + 13/6 = (5 + 4) / (5 - 2)
18/6 = 9/3
3 = 3
