Question

\(1-\frac{\frac{2}{19}+\frac{2}{43}-\frac{2}{2013}}{\frac{3}{19}+\frac{3}{43}-\frac{3}{2013}}\)

Answer 1

\(1-\frac{\frac{2}{19}+\frac{2}{43}-\frac{2}{2013}}{\frac{3}{19}+\frac{3}{43}-\frac{3}{2013}}\)= \(1-\frac{2\left(\frac{1}{19}+\frac{1}{43}-\frac{1}{2013}\right)}{3\left(\frac{1}{19}+\frac{1}{43}-\frac{1}{2013}\right)}\)= 1 - \(\frac{2}{3}\)=\(\frac{1}{3}\)

Answer 2

\(1-\frac{\frac{2}{19}+\frac{2}{43}-\frac{2}{2013}}{\frac{3}{19}+\frac{3}{43}-\frac{3}{2013}}=1-\frac{2\left(\frac{1}{19}+\frac{1}{43}-\frac{1}{2013}\right)}{3\left(\frac{1}{19}+\frac{1}{43}-\frac{1}{2013}\right)}\)=\(1-\frac{2}{3}=\frac{1}{3}\)