prove that m(n+1)+1/m(n+1)-n cannot be simplified

Question

topics including real numbers

Answer 1

(m(n+1)+1)/(m(n+1)-n)=

((m(n+1)-n)+n+1)/(m(n+1)-n)=

1+(n+1)/(m(n+1)-n)=

1+1/(m-n/(n+1)).

n/(n+1) for general n cannot be simplified—it is always a fraction. So the original expression cannot be simplified.