Question

[abcdegh]

\(\left(\frac{1}{7}+\frac{1}{23}-\frac{1}{1009}\right)\): \(\left(\frac{1}{23}+\frac{1}{7}-\frac{1}{1009}+\frac{1}{7}\cdot\frac{1}{23}\cdot\frac{1}{1009}\right)\)+ \(\frac{1}{30\cdot1009-160}\)

Answer 1

[Thanh Tùng DZ]

đặt A là tên biểu thức trên

ta có :

\(A=\left(\frac{1}{7}+\frac{1}{23}-\frac{1}{1009}\right):\left(\frac{1}{23}+\frac{1}{7}-\frac{1}{1009}+\frac{1}{7}.\frac{1}{23}.\frac{1}{1009}\right)+\frac{1}{30.1009-160}\)

\(A=\left(\frac{23.1009}{7.23.1009}+\frac{7.1009}{7.23.1009}-\frac{7.23}{7.23.1009}\right):\left(\frac{7.1009}{23.7.1009}+\frac{23.1009}{23.7.1009}-\frac{23.7}{23.7.1009}+\frac{1}{23.7.1009}\right)+\frac{1}{30.1009-160}\)\(A=\frac{23.1009+7.1009-7.23}{7.23.1009}:\frac{7.1009+23.1009-23.7+1}{7.23.1009}+\frac{1}{30.1009-160}\)

\(A=\frac{23.1009+7.1009-7.23}{7.1009+23.1009-23.7+1}+\frac{1}{30.1009-160}\)

\(A=\frac{30.1009-161}{30.1009-160}+\frac{1}{30.1009-160}\)

\(A=\frac{30.1009-160}{30.1009-160}=1\)

Answer 2

[Phạm Duy Minh]

nhân hai số đầu với bình phương 23.7.1009 ta có 30109/30110+1/30110=1