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.