Question

cho P = (\(\frac{\sqrt{y}}{\sqrt{y}-1}-\frac{1}{y-\sqrt{y}})\) : \(\left(\frac{1}{\sqrt{y}+1}+\frac{2}{y-1}\right)\)

Rút gọn P và tìm y để P < 1

Answer 1

P = \(\frac{\sqrt{y}.\sqrt{y}-1}{\sqrt{y}\left(\sqrt{y}-1\right)}:\frac{1\left(\sqrt{y}-1\right)+2}{\left(\sqrt{y}-1\right)\left(\sqrt{y}+1\right)}\)

P = \(\frac{y-1}{\sqrt{y}\left(\sqrt{y}-1\right)}:\frac{\sqrt{y}+1}{\left(\sqrt{y}+1\right)\left(\sqrt{y}-1\right)}\)

P = \(\frac{y-1}{\sqrt{y}\left(\sqrt{y}-1\right)}.\frac{\left(\sqrt{y}-1\right)\left(\sqrt{y}+1\right)}{\sqrt{y}+1}=\frac{y-1}{\sqrt{y}}\)

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