Prove or disprove,n is a rational number, 1/n does not equal n-1

Question

Prove or disprove,n is a rational number, 1/n ≠ n-1

Answer 1

John,

 

You were given a good proof at

 

https://www.wyzant.com/resources/answers/254029/prove_1_n_n_1

Answer 2

Suppose 1/n=n-1. By cross multiplication, n(n-1)=1. n^2-n-1=0. solutions of this equation are irrationals. Hence, it is prove that, if n is a rational number, 1/n does not equal n-1.