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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

 Mar 13, 2021
 #1
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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

 

cool cool cool

 Mar 13, 2021

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