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Find all real values of x that satisfy \(\frac{1}{x(x+1)}-\frac{1}{(x+1)(x+2)} < \frac{1}{3}\) . Give your answer in interval notation.

 Dec 26, 2019
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Multiplying both sides by 3x(x + 1)(x + 2): 3(x + 2) - 3x < (x + 1)(x + 2).

 

Simplify: x^2 + 3x - 4 > 0

 

Factor: (x + 4)(x - 1) > 0

 

Solution: (-inf,-4) U (1,inf)

 Dec 26, 2019

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