book Maths Puzzle Numerical Ability

I am having trouble with a question, Add the fractions

q
--------
q^2+5q+6

and

1
--------
q^2+3q+2


I think the answer is

q^2+2q+3
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book Other Question

The combined cost of one advance ticket to a show and one same-day ticket was $55. It is known that 30 tickets were sold in advance and 25 the same day, for total receipts of $1575 . What was the price of each kind of ticket? x^2+2x+3=0