Question 972769
original fraction is (x-5) / x


when you multiply the numerator by 2 and add 16 to the denominator, the original fraction is reduced by 1/3.


this means the original fraction is equal to 2/3 times what it was originally.


your equation is:


(x-5) * 2 divided by x + 16
is equal to 2/3 * (x-5) / x


 this is equivalent to:


(x-5) * 2 / (x + 16) = ((x-5) * 2) / 3x


multiply both sides of the equation by (x+16) and by (3x) and you get:


(x-5) * 2 * (3x) = (x-5) * 2 * (x+16) 


divide both sides of this equation by (x-5) and you get:


2 * 3x = 2 * (x + 16)


simplify to get:


6x = 2x + 32


subtract 2x from both sides of this equation to get:


4x = 32


divide both sides of this equation by 4 to get:


x = 8


that's your solution.


your original fraction is (8-5)/8 = 3/8


your final fraction is (3 * 2) / (8 + 16) = 6 / 24 = 1/4


your original fraction of 3/8 * 2/3 = 6/24 = 1/4.


this is the same as your original fraction being reduced by 1/3.


3/8 - 1/3 * 3/8 = 3/8 - 3/24 = 9/24 - 3/24 = 6/24 = 1/4.


the questions was what is the original fraction.


the answer is that the original fraction is 3/8.