Để rút gọn được phân số \(\frac{63}{x+1}\) thì:
\(63⋮x+1\)
\(\Rightarrow x\inƯ\left(63\right)\)
\(\RightarrowƯ\left(63\right)=\left\{1;3;7;9;21;63\right\}\)
\(\Rightarrow x=\left\{\begin{matrix}x+1=1\Rightarrow x=1-1=0\\x+1=3\Rightarrow x=3-1=2\\x+1=7\Rightarrow x=7-1=6\end{matrix}\right.\)
\(\Rightarrow x=\left\{\begin{matrix}x+1=9\Rightarrow x=9-1=8\\x+1=21\Rightarrow x=21-1=20\\x+1=63\Rightarrow x=63-1=62\end{matrix}\right.\)
\(\Rightarrow x=\left\{0;2;6;8;20;62\right\}\)
\(x\inƯC\left(63\right)\)
Ư(63) = { 1 ; 3 ; 7; 9 ; 21 ; 63 }
x + 1 thuộc Ư(63) => x = 1- 1 = 0
x = 3 - 1 = 2
x = 7 - 1 = 6
x = 9 - 1 = 8
x = 21 - 1 = 20
x = 63 - 1 = 62
=> \(x\in\left\{0;2;6;8;20;62\right\}\)
\(63⋮x+1\)
\(\Rightarrow x+1\inƯ\left(63\right)\)
Mà \(Ư\left(63\right)=\left\{1;3;7;9;21;62\right\}\)
\(x+1\in\left\{1;3;7;9;21;63\right\}\)
\(\Rightarrow x\in\left\{0;2;6;8;20;62\right\}\)