the complete question is
If we add 5 to the denominator And subtract 5 from the numerator of a fraction ot reduces to 1/7. if we subtract 3 from the numerator and add 3 to its denominator ot reduces to 1/3. find the fraction.
Let
x/y-----------> the fraction
we know that
(x-5)/(y+5)=1/7------>7*(x-5)=(y+5)-----> y=7x-35-5----> y=7x-40----> equation 1
(x-3)/(y+3)=1/3----> 3*(x-3)=y+3----> y=3x-9-3----> y=3x-12------> equation 2
equate equation 1 and equation 2
7x-40=3x-12-----> 7x-3x=40-12------> 4x=28-----> x=7
y=3x-12------> y=3*7-12-----> y=9
x/y=7/9
the answer is
the fraction is 7/9
