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Question Number 166358 by leicianocosta last updated on 19/Feb/22

Answered by naka3546 last updated on 19/Feb/22

((3a^2 +5)/(a^2 −1)) − ((3a^2 +1)/(a^2 −1)) < 0                        (4/(a^2 −1)) < 0  2( (1/(a−1)) − (1/(a+1)) ) < 0        −1 < a < 1

$$\frac{\mathrm{3a}^{\mathrm{2}} +\mathrm{5}}{\mathrm{a}^{\mathrm{2}} −\mathrm{1}}\:−\:\frac{\mathrm{3a}^{\mathrm{2}} +\mathrm{1}}{\mathrm{a}^{\mathrm{2}} −\mathrm{1}}\:<\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{4}}{\mathrm{a}^{\mathrm{2}} −\mathrm{1}}\:<\:\mathrm{0} \\ $$$$\mathrm{2}\left(\:\frac{\mathrm{1}}{\mathrm{a}−\mathrm{1}}\:−\:\frac{\mathrm{1}}{\mathrm{a}+\mathrm{1}}\:\right)\:<\:\mathrm{0} \\ $$$$\:\:\:\:\:\:−\mathrm{1}\:<\:\mathrm{a}\:<\:\mathrm{1} \\ $$

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