Toán Lớp 9: (( √a + √b / √a – √b )- (4 √ab/a-b)) × ( a √a +b √b)/ (√ab – (a+b)))
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Toán Lớp 9: (( √a + √b / √a – √b )- (4 √ab/a-b)) × ( a √a +b √b)/ (√ab – (a+b)))
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DK:a > 0;b > 0\\
\left( {\dfrac{{\sqrt a + \sqrt b }}{{\sqrt a – \sqrt b }} – \dfrac{{4\sqrt {ab} }}{{a – b}}} \right).\dfrac{{a\sqrt a + b\sqrt b }}{{\sqrt {ab} – a – b}}\\
= \left[ {\dfrac{{{{\left( {\sqrt a + \sqrt b } \right)}^2} – 4\sqrt {ab} }}{{\left( {\sqrt a – \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}} \right].\dfrac{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a – \sqrt b } \right)}}{{ – \left( {a – \sqrt {ab} + b} \right)}}\\
= \dfrac{{a + 2\sqrt {ab} + b – 4\sqrt {ab} }}{{\left( {\sqrt a – \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}.\dfrac{{\left( {\sqrt a + \sqrt b } \right)\left( {\sqrt a – \sqrt b } \right)}}{{ – \left( {a – \sqrt {ab} + b} \right)}}\\
= \dfrac{{a – 2\sqrt {ab} + b}}{{ – \left( {a – \sqrt {ab} + b} \right)}}
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