Question

[Nga Văn]

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

Answer 1

[Nga Văn]

giúp mình câu 1 trước đi nè

Answer 2

[Huong San]

Câu 2:

a, ĐKXĐ: x\(\ge\)0; x\(\ne\)\(\pm\)1

B=

\(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{-2.2\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{-4\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{4\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}.\dfrac{\sqrt{x}+1}{\sqrt{x}}\\ =-\dfrac{4}{\sqrt{x}-1}\)