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Гость[latex] \frac{a-b}{a^{1/2}-b^{1/2}} - \frac{a^{3/2}-b^{3/2}}{a-b} = \frac{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})}{a^{1/2}-b^{1/2}} - \frac{(a^{1/2}-b^{1/2})(a+a^{1/2}b^{1/2}+b)}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})}= \\\\= \frac{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})^2}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})} -\frac{(a^{1/2}-b^{1/2})(a+a^{1/2}b^{1/2}+b)}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})} =\\\\= \frac{(a^{1/2}-b^{1/2})(a+2a^{1/2}b^{1/2}+b-a-a^{1/2}b^{1/2}-b)}{(a^{1/2}-b^{1/2})(a^{1/2}+b^{1/2})}=[/latex]
=[latex] \frac{a^{1/2}b^{1/2}}{a^{1/2}+b^{1/2}}} = \frac{ \sqrt{a}* \sqrt{b} }{ \sqrt{a} + \sqrt{b} } [/latex]
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