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Given s > r > 1. I suppose this is missed in the question given.

let us take the expression:

E = r ( s - r + 1) - s

= r s - r² + r - s

= s (r - 1) - r² + r

= s (r - 1) - r (r - 1)

= (s - r ) (r - 1) => this is positive as s > r and r > 1

Hence the expression E is positive. proves the given question as E > 0

let us take the expression:

E = r ( s - r + 1) - s

= r s - r² + r - s

= s (r - 1) - r² + r

= s (r - 1) - r (r - 1)

= (s - r ) (r - 1) => this is positive as s > r and r > 1

Hence the expression E is positive. proves the given question as E > 0