Let the numerator be n; the fraction is:
[tex]\frac{n}{n+2}[/tex]
The denominator of a fraction is two more than the numerator. If both numerator and denominator are increased by one; then:
[tex]\frac{n+1}{n+3}[/tex]
The simplified result is 6/7; then:
[tex]\frac{n+1}{n+3}=\frac{6}{7}[/tex]
Solving for n:
(n + 1) x 7 = (n + 3) x 6
7n + 7 = 6n + 18
7n - 6n = 18 - 7
n = 11
The original fraction is:
[tex]\frac{11}{13}[/tex]
