Question 165928
fraction is (x-1)/x
fraction with numerator and denominator increased by 2 is (x+1)/(x+2)

the fraction is increased by 1/12

then  (x-1)/x  + 1/12  = (x+1)/(x+2)


(12(x-1)+x)/12x = (x+1)/(x+2)
(13x-12)/12x = (x+1)/(x+2)

(13x-12)(x+2)=12x(x+1)

13x^2+14x-24=12x^2+12x
x^2+2x-24=0
{{{x = (-2 +- sqrt( 2^2-4*1*(-24) ))/(2) }}} 
then

{{{x = (-2 +- 10 )/(2) }}} 

x=-6 or x=4

assuming numerator and denominator possitive

then x=4 and fraction is 3/4