Question

1. Rút gọn rồi quy đồng mẫu các phân số sau :

\(C=\frac{1010}{1008.8-994};D=\frac{1.2.3+2.4.6+3.6.9+5.10.15}{1.3.6+2.6.12+1.9.18+5.15.30}\)

2. Tìm số nguyên x biết : 

\(\frac{2x-9}{240}=\frac{39}{80}\)

Cần gấp lắm ak

Answer 1

\(\frac{2x-9}{240}=\frac{39}{80}\)

\(\Rightarrow\left(2x-9\right).80=240.39\)

       \(160x-720=9360\)

       \(160x=9360+720\)    

       \(160x=10080\)

               \(x=10080:160\)

               \(x=63\)

Vậy x=63

Answer 2

1. Ta có : \(C=\frac{1010}{1008\cdot8-994}=\frac{1010}{\left(1010-2\right)\cdot8-994}=\frac{1010}{1010\cdot8-16-994}\)

\(=\frac{1010}{1010\cdot8-1010}=\frac{1010}{1010\left(8-1\right)}=\frac{1}{7}\)

\(D=\frac{1\cdot2\cdot3+2\cdot4\cdot6+3\cdot6\cdot9+5\cdot10\cdot15}{1\cdot3\cdot6+2\cdot6\cdot12+3\cdot9\cdot18+5\cdot15\cdot30}\)

\(D=\frac{1\cdot2\cdot3+2\cdot4\cdot6+3\cdot6\cdot9+5\cdot10\cdot15}{1\cdot2\cdot3\cdot3+2\cdot4\cdot6\cdot3+3\cdot6\cdot9\cdot3+5\cdot10\cdot15\cdot3}\)

\(D=\frac{1\cdot2\cdot3+2\cdot4\cdot6+3\cdot6\cdot9+5\cdot10\cdot15}{3\left(1\cdot2\cdot3+2\cdot4\cdot6+3\cdot6\cdot9+5\cdot10\cdot15\right)}=\frac{1}{3}\)

2. \(\frac{2x-9}{240}=\frac{39}{80}\)

=> \(\frac{2x-9}{240}=\frac{39\cdot3}{80\cdot3}=\frac{117}{240}\)

=> 2x - 9 = 117

=> 2x = 117 + 9 = 126

=> x = 126 : 2 = 63