Toán Lớp 9: Rút gọn các biểu thức sau
A= √a + √b /2 √a -2 √b – √a- √b/2 √a -2 √b -2b /b-a
B= (x√x – 1 / √x+1 + x √x +1/x+ √x): (2(x-2 √x +1)/ x-1)
Mọi người làm giúp mình với ạ mình cảm ơn mình đang cần gấp . Hôm nay mình thi rồi
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A = \dfrac{{\sqrt a + \sqrt b }}{{2\sqrt a – 2\sqrt b }} – \dfrac{{\sqrt a – \sqrt b }}{{2\sqrt a – 2\sqrt b }} – \dfrac{{2b}}{{b – a}}\\
= \dfrac{{\sqrt a + \sqrt b – \sqrt a + \sqrt b }}{{2\left( {\sqrt a – \sqrt b } \right)}} + \dfrac{{2b}}{{a – b}}\\
= \dfrac{{2\sqrt b }}{{2\left( {\sqrt a – \sqrt b } \right)}} + \dfrac{{2b}}{{\left( {\sqrt a – \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}\\
= \dfrac{{\sqrt b .\left( {\sqrt a + \sqrt b } \right) + 2b}}{{\left( {\sqrt a – \sqrt b } \right)\left( {\sqrt a + \sqrt b } \right)}}\\
= \dfrac{{\sqrt {ab} + 3b}}{{a – b}}\\
B = \left( {\dfrac{{x\sqrt x – 1}}{{\sqrt x + 1}} + \dfrac{{x\sqrt x + 1}}{{x + \sqrt x }}} \right):\left( {\dfrac{{2\left( {x – 2\sqrt x + 1} \right)}}{{x – 1}}} \right)\\
= \left( {\dfrac{{\left( {x\sqrt x – 1} \right).\sqrt x + x\sqrt x + 1}}{{\sqrt x \left( {\sqrt x + 1} \right)}}} \right)\\
:\dfrac{{2{{\left( {\sqrt x – 1} \right)}^2}}}{{\left( {\sqrt x – 1} \right)\left( {\sqrt x + 1} \right)}}\\
= \dfrac{{{x^2} – \sqrt x + x\sqrt x + 1}}{{\sqrt x \left( {\sqrt x + 1} \right)}}.\dfrac{{\sqrt x + 1}}{{2\left( {\sqrt x – 1} \right)}}\\
= \dfrac{{{x^2} + x\sqrt x – \sqrt x + 1}}{{2\sqrt x \left( {\sqrt x – 1} \right)}}
\end{array}$