book Maths Puzzle Numerical Ability

x^2+2x+3=0

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book Other Question

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
---------- can you help me solve (x+2)(x-3)=(x-3)^2