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Prove that (n!)/(r!(n-r)!)+(n!)/((r-1)...

Prove that
`(n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!) =((n+1)!)/(r!(n-r+1)!)`

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To prove the equation \[ \frac{n!}{r!(n-r)!} + \frac{n!}{(r-1)!(n-r+1)!} = \frac{(n+1)!}{r!(n-r+1)!} \] we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS). ...
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