Question

the numerator of a fraction is 6 less than the denominator if 3 is added to the numerator the fraction is equal to 2 by 3 then the original fraction is

Answer 1

let the numerator of fraction= X

and denominator of fraction= Y

according to question,

X/Y is a fraction..

x-6/Y ( because 6 is less than the denominator)

now adding by 3 in numerator

X-6+3/Y=2/3

X-3/Y= 2/3

3x-9=2y

hope it help you

Answer 2

let x/y be the original fraction

x = numerator
y = denominator

the numerator of a fraction is 6 less than the denominator

x = y - 6

if 3 is added to the numerator, the fraction is equal to 2/3

(x + 3)/y = 2/3 cross multiply
3(x + 3) = 2y

by solving the system of equations

x = y - 6
3(x + 3) = 2y

we find

x = 3
y = 9