The denominator of the fraction is four more than the numerator. The fraction:
[tex]\frac{x}{x+4}[/tex]
If both numerator and denominator are increased by eight, the simplified result is 5/6:
[tex]\frac{x+8}{x+4+8}=\frac{5}{6} \\ \\
\frac{x+8}{x+12}=\frac{5}{6} \ \ \ |\times (x+12) \\ \\
x+8=\frac{5}{6}x+\frac{5}{6} \times 12 \\ \\
x+8=\frac{5}{6}x+10 \\ \\
x-\frac{5}{6}x=10-8 \\ \\
\frac{1}{6}x=2 \ \ \ |\times 6 \\ \\
x=12 \\ \\
\frac{x}{x+4}=\frac{12}{12+4}=\boxed{\frac{12}{16}}[/tex]
The original fraction is 12/16.
