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Simplify and State Restrictions: 2/(x^2+7x+12) + 5/(x^2+5x+6)?

My answer is as follows:

2/(x+3)(x+4) + 5/(x+2)(x+3)

= (2(x+3)(x+2))/((x+2)(x+3)(x+4)) + (5(x+3)(x+4))/((x+2)(x+3)(x+4))

= (2(x^2+2x+3x+6))/((x+2)(x+3)(x+4))+(5(x^2+4x+3x+12))/(x+2)(x+3)(x+4)

= (2x^2+10x+12)/((x+2)(x+3)(x+4)) + ((5x^2+35x+60)/(x+2)(x+3)(x+4))

Final Answer being:

(7x^2+45x+72) / ((x+2)(x+3)(x+4))

Restrictions are: x cannot be -2, -3, -4

Am I Right?

Thanks in Advance!

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