For fist case let the fraction is x/y;

than 4 is added to numerator and denominator the fraction will be equal to 18/10;

(x+4) / (y+4) = 18 / 10

(x+4) / (y+4) = 18/10;

10x +40 = 18y + 72

10x - 18y = 32

5x - 9y = 16 -------(1)

 

than 6 is subtracted to numerator and denominator the fraction will be equal to 8/5;

(x - 6) / (y - 6) = 8 / 5;

5x - 30 = 8y - 48

5x - 8y = -18 -------(2)

 

by solving equation 1 and 2 by elemination method;

5x - 9y = 16

-5x + 8y = +18 ( changing the sign od second equation)

adding both equations we get

-y = 34;

y = -34

than x= 5x - 8 * (-34) = -18

5x = -290

x = -58

x/y = -58/-34