Question

1/x-1 > 1/x+1, solve for x, graph it on the number line (wavy curve method) and find what x belongs to (rational inequality)

Answer 1

Answer:

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Answer 2

Answer:

The wavy curve method (also called the method of intervals) is a strategy used to solve inequalities of the form \frac{f(x)}{g(x)} > 0g(x)f(x)>0 \left(<0, \, \geq 0, \, \text{or} \, \leq 0\right).(<0,≥0,or≤0). The method uses the fact that \frac{f(x)}{g(x)}g(x)f(x) can only change sign at its zeroes and vertical asymptotes, so we can use the roots of f(x)f(x) and g(x)g(x) to sketch a graph of the function over different intervals.