prove the combinatorial identity: $ {2n \choose n} + {2n\choose n-1} = (1/2){2n + 2 \choose n + 1}$ So the first thing I did was to multiply and then isolate the left-most term. 
That leaves me with  $$ 2{2n \choose n} ={2n + 2\choose n + 1} - 2{2n \choose n -1} $$
No specific reasoning except that it looks cleaner, at least to me. Then the way I thought about it was that we are trying to make two $n$ member committees out of $n$ koalas and $n$ pandas. I was told when seeing subtraction I should think of complement but I don't really know how to incorporate the complement into this. Any way, am I on the right path or completely off. Thank you in advance for your time. 

Hint: Use the identity
$$\binom{2n}{n}+\binom{2n}{n-1}=\binom{2n+1}{n}.$$
And the (algebraic) definition of binomial coefficient.
