Question

Tính nhanh: \(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)

Answer 1

\(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(\frac{-12}{1999}-\frac{12}{2011}\right)\)

\(=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)

\(=\left(\frac{1999}{2011}+\frac{12}{2011}\right)+\left(\frac{-2011}{1999}+\frac{12}{1999}\right)=\frac{2011}{2011}-\frac{1999}{1999}=1-1=0\)

Answer 2

\(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(-\frac{12}{1999}-\frac{12}{2011}\right)\)

\(=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}\)

\(=\left(\frac{1999}{2011}+\frac{12}{2011}\right)+\left(-\frac{2011}{1999}+\frac{12}{1999}\right)\)

\(=1+\left(-1\right)\)

\(=0\)

Answer 3

\(\left(\frac{1999}{2011}-\frac{2011}{1999}\right)-\left(-\frac{12}{1999}-\frac{12}{2011}\right)=\frac{1999}{2011}-\frac{2011}{1999}+\frac{12}{1999}+\frac{12}{2011}=\frac{1999}{2011}-1+\frac{12}{2011}=-\frac{12}{2011}+\frac{12}{2011}=0\)