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Show that: `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`

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#### Solution

L.H.S. = `(9!)/(3!6!) + (9!)/(4!5!)`

= `(9!)/(3!xx6 xx 5!) + (9!)/(4 xx 3! xx 5!)`

= `(9!)/(5!3!) [1/6 + 1/4]`

= `(9!)/(5! xx 3!)[(4 + 6)/(6xx4)]`

= `(9!xx10)/(6xx5!xx4xx3!)`

= `(10!)/(6!4!)`

= `(10!)/(4!6!)`

= R.H.S.

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