find a way to overcome $\frac{1-x}{1+x}-\frac{1}{3x+1}$ loss of significance
- for which values is there loss of significance? is it 0
- to solve it I get need to multiply it by $\frac{\frac{1-x}{1+x}+\frac{1}{3x+1}}{\frac{1-x}{1+x}+\frac{1}{3x+1}}$?
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1There is loss of significance near where the two fractions are equal, that is, $x=0$ or $x=1/3$. – lhf Dec 29 '16 at 20:52
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How about $\dfrac{x - 3 x^2}{3 x^2 + 4 x + 1}$? – lhf Dec 29 '16 at 20:56
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@lhf just to use a common denominator? – gbox Dec 29 '16 at 20:59
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Just compute the difference, and note that it is equal $-\frac{x}{1+x}$ so it becomes indefinite when $x=-1$.
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