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Solve for real x: 1/(x + 1) + 2/(x + 2) > 3/(x + 3).

1. x in (-infinity, -3) U (-2, -3/2) U (-1, infinity)
2. x in (-3, -2) U (-3/2, -1)
3. x in (-infinity, -3) U (-1, infinity)
4. x in (-2, infinity)

Correct answer: x in (-infinity, -3) U (-2, -3/2) U (-1, infinity)

Solution

Move the right side over, combine to a single fraction, find its numerator roots and the excluded points, then use a sign chart across the critical values.

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