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Question Number 174579 by behi834171 last updated on 04/Aug/22

    find minimum value of:             ((a^2 (b−1)^2 +2ab+(a−1)^2 )/(a(ab+1)))         [all∈R]

$$\:\:\:\:{find}\:{minimum}\:{value}\:{of}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\boldsymbol{{a}}^{\mathrm{2}} \left(\boldsymbol{{b}}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\boldsymbol{{ab}}+\left(\boldsymbol{{a}}−\mathrm{1}\right)^{\mathrm{2}} }{\boldsymbol{{a}}\left(\boldsymbol{{ab}}+\mathrm{1}\right)}\:\:\:\:\:\:\:\:\:\left[\boldsymbol{{all}}\in\boldsymbol{{R}}\right] \\ $$

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