câu 1 rút gọn
A=\(\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}+\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{3}-\sqrt{2}}\)
B=\(\dfrac{2}{\sqrt{3}-\sqrt{5}}+\dfrac{3-2\sqrt{3}}{\sqrt{3}-2}\)
C = \(\dfrac{\sqrt{2}+1}{\sqrt{5+2\sqrt{6}}}+\dfrac{2}{\sqrt{8}+2\sqrt{15}}\)
Câu 2 cho pt
B= \(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+1}\)
a, tìm ĐKXĐ và rút gọn
b, tính B khi x =\(3+2\sqrt{2}\)
c, tìm x để B nguyên
Câu 2:
a, ĐKXĐ: x\(\ge\)0; x\(\ne\)\(\pm\)1
B=
\(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{-2.2\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{-4\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{4\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}.\dfrac{\sqrt{x}+1}{\sqrt{x}}\\ =-\dfrac{4}{\sqrt{x}-1}\)
Câu 1:
a: \(=\dfrac{-5+2\sqrt{6}+5+2\sqrt{6}}{1}=4\sqrt{6}\)
b: \(=\dfrac{2\left(\sqrt{3}+\sqrt{5}\right)}{-2}+\dfrac{\sqrt{3}\left(\sqrt{3}-2\right)}{\sqrt{3}-2}\)
\(=-\sqrt{3}-\sqrt{5}+\sqrt{3}=-\sqrt{5}\)
c: \(=\dfrac{\sqrt{2}+1}{\sqrt{3}+\sqrt{2}}+\dfrac{2}{\sqrt{5}+\sqrt{3}}\)
\(=\left(\sqrt{2}+1\right)\left(\sqrt{3}-\sqrt{2}\right)+\sqrt{5}-\sqrt{3}\)
\(=\sqrt{6}-2+\sqrt{3}-\sqrt{2}+\sqrt{5}-\sqrt{3}\)
\(=\sqrt{6}-2-\sqrt{2}+\sqrt{5}\)