Question 1043253
Let n = numerator
Let d = denominator
d = n-7
fraction is {{{n/(n-7)}}}
{{{n/(n-7)+(1+1/3)=14/9}}}
{{{n/(n-7)+(4/3)=14/9}}}
add -4/3 to each side
{{{n/(n-7)=(14/9)-(4/3)}}}
{{{n/(n-7)=(14/9)-(12/9)}}}
{{{n/(n-7)=(2/9)}}}
do cross products
9n = 2(n-7)
9n = 2n -14
add -2n to each side
7n = -14
divide each side by 7
n = -2
So the original fraction is {{{(-2)/(-9)}}}