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Hello. I'm currently working my way through Lang's Basic Mathematics and cannot make sense of this question:

Show that if n is a positive integer at most equal to m, then

Show that if n is a positive integer at most equal to m, then

[tex]{m \choose n}+{m\choose n-1}={m+1 \choose n}[/tex]

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The answer in the textbook is given as:

**1**. [tex]{m \choose n}+{m\choose n-1}={m! \over n!(m-n)!}+{m! \over (m-n+1)!(n-1)}[/tex]

[common denominator n!(m — n + 1)!]

**2.**[tex]= {m!(m-n+1)+m!n\over n!(m-n+1)!}[/tex]

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I omitted the rest of the answer as I understand what follows from

**2.**

However I don't understand how to get such denominator from

**1.**

Could someone please help me?

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