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The denominator of a fraction is four more than the numerator. If both numerator and denominator are increased by eight, the simplified result is 5/6. Find the original fraction.

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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.
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