Answer:
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I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,
One possible answer is 
Another possible answer is 
There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)
So in the first example above, we would have

In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.
Similar steps will happen with the second example as well (when g(x) = x^2)
Everyone works differently in mental meth.
To calculate 9*52, we note that 9=10-1, so mentally calculate
9(52)
=(10-1)(52)
=520-52 [ subtract 20 from each number]
=(520-20)-(52-20)
=500-32
=468.
Alternatively,
9*52=9*50+9*2=450+18=468
If you're good with multiplication and division,
9*52=3*3(52)=3*156=450+18=468
notice the first term is -10, and the common difference is 3, so we add 3 to get the next term.

check the picture below.