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Question Number 146608 by mathdanisur last updated on 14/Jul/21

$$\frac{x\sqrt{x}-1}{x+\sqrt{x}+1}:\frac{\sqrt{x}-1}{\sqrt{x}+1}=?$$

Answered by qaz last updated on 15/Jul/21

$$\frac{\mathrm{x}\sqrt{\mathrm{x}}-1}{\mathrm{x}+\sqrt{\mathrm{x}}+1}:\frac{\sqrt{\mathrm{x}}-1}{\sqrt{\mathrm{x}}+1}=\frac{{\mathrm{a}}^3-1}{{\mathrm{a}}^2+\mathrm{a}+1}:\frac{\mathrm{a}-1}{\mathrm{a}+1}$$$$=\frac{{\mathrm{a}}^2+\mathrm{a}+1}{{\mathrm{a}}^2+\mathrm{a}+1}:\frac{1}{\mathrm{a}+1}=\mathrm{a}+1=\sqrt{\mathrm{x}}+1$$

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