Упростите выражение ((2÷√a-√b)-(2√a÷a√a+b√b)·(a-√ab+b÷√a-√b))÷4√b. Created by 81saida. matematika-ru

Упростите выражение ((2÷√a-√b)-(2√a÷a√a+b√b)·(a-√ab+b÷√a-√b))÷4√b...

August 2022 1 14 Report

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((2÷√a-√b)-(2√a÷a√a+b√b)·(a-√ab+b÷√a-√b))÷4√b

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tamarabernukho $( \frac{2}{ \sqrt{a}- \sqrt{b} } - \frac{2 \sqrt{a} }{a \sqrt{a}+b \sqrt{b} } * \frac{a- \sqrt{ab} +b}{ \sqrt{a}- \sqrt{b} } ):4 \sqrt{b} = \\ \\ \frac{2a \sqrt{a} +2b \sqrt{b} -2 \sqrt{a}(a- \sqrt{ab} +b) }{( \sqrt{a}- \sqrt{b} )( a \sqrt{a}+b \sqrt{b}) } :4 \sqrt{b} = \\ \\ \frac{2a \sqrt{a} +2b \sqrt{b} -2a \sqrt{a}+2a \sqrt{b} -2 \sqrt{a} b }{( \sqrt{a}- \sqrt{b} )( a \sqrt{a}+b \sqrt{b}) } :4 \sqrt{b} = \\ \\$

$\frac{ 2b \sqrt{b} +2a \sqrt{b} -2 \sqrt{a} b }{( \sqrt{a}- \sqrt{b} )( a \sqrt{a}+b \sqrt{b}) } :4 \sqrt{b} = \\ \\ \frac{ 2 b ( b+a- \sqrt{ab}) }{4 ( \sqrt{a}- \sqrt{b} )( a \sqrt{a}+b \sqrt{b}) } = \\ \\ \frac{ b(b+a- \sqrt{ab} )}{2 ( \sqrt{a}- \sqrt{b} )( a \sqrt{a}+b \sqrt{b}) } \\ \\ \\$
$= \frac{b(a- \sqrt{ab} +b)}{2( \sqrt{a}- \sqrt{b} )( \sqrt{a} + \sqrt{b} )(a- \sqrt{ab} +b )} = \frac{b}{2a-2b} \\ \\$

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