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Prove that ^(n-1) Pr+r .^(n-1) P(r-1) = ...

Prove that `^(n-1) P_r+r .^(n-1) P_(r-1) = .^nP_r`

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`.^(n-1)P_(r )+r^(n-1)P_(r-1)=((n-1)!)/((n-1-r)!)+r((n-1)!)/((n-r)!)`
`=((n-1)!)/((n-1-r)!){1+r(1)/(n-r)}`
`=((n-1)!)/((n-1-r)!)((n)/n-r)`
`=(n!)/((n-r)!)=.^(n)P_(r )`
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