Question 1064373
let x be the original numerator.
let y be the original denominator.


you get x/y = 3/4


when you add 4 to the numerator and subtract 8 from the denominator, you get:


(x + 4) / (y - 8) = 1


solve for x in the first equation to get x = 3/4 * y


replace x in the second equation with 3/4 * y to get:


(3/4 * y + 4) / (y - 8) = 1


multiply both sides of this equation to get:


3/4 * y + 4 = y - 8


subtract 4 from both sides of the equation to get:


3/4 * y = y - 12


subtract y from both sides of this equation to get:


-1/4 * y = -12


solve for y to get y = 48


go back to the original equation of x/y = 3/4 and replace y with 48 to get:


x/48 = 3/4


multiply both sides of this equation by 48 to get:


x = (3 * 48) / 4 = 3 * 12 = 36


you get x = 36 and y = 48


x/y = 36/48 = 3/4


(x+4) / (y-8) = (36+4) / (48-8) = 40/40 = 1


solution looks good.


the original fraction is 36/48.