Question

Mn giải jum mk nha:

Chứng minh \(\frac{n^3-1}{n^5+n+1}\) không tối giản

 

Answer 1

\(\frac{n^3-1}{n^5+n+1}\)

\(=\frac{\left(n-1\right)\left(n^2+n+1\right)}{n^5-n^2+n^2+n+1}\)

\(=\frac{\left(n-1\right)\left(n^2+n+1\right)}{n^2\left(n^3-1\right)+n^2+n+1}\)

\(=\frac{\left(n-1\right)\left(n^2+n+1\right)}{n^2\left(n-1\right)\left(n^2+n+1\right)+n^2+n+1}\)

\(=\frac{\left(n-1\right)\left(n^2+n+1\right)}{\left(n^2+n+1\right)\left[n^2\left(n-1\right)+1\right]}\)

Vì n²+n+1 chia hết cho chính nó

=> đpcm