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Simplify and State Restrictions: (2/x^2+7x+12)+(5/x^2+5x+6)?
I was able to factor the denominators, so it looks like:
2/(x+4)(x+3) + 5/(x+1)(x+6)
From there, I know I have to determine the lowest common denominator, but with factored form denominators of a simple trinomial, I'm not sure how to go about with it.
1 Answer
- anonymousLv 78 months agoFavorite Answer
The factored form of the second denominator is incorrect. It should be
x² + 5x + 6 = (x + 2)(x + 3)
so for the whole thing you would have
[2 / (x + 4)(x + 3)] + [5 / (x + 2)(x + 3)]
To get a common denominator, which will be [(x + 4)(x + 3)(x + 2)], you would multiply the first term by 1 = [(x + 2) / (x + 2)] and multiply the second term by 1 = [(x + 4) / (x + 4)] to get
[2(x + 2) + 5(x + 4)] / [(x + 4)(x + 3)(x + 2)]
x = -2, -3, and -4 are excluded from the domain because they make the denominator equal to zero.
Graph: