Question

cho pt (\(\dfrac{\sqrt{x}}{\sqrt{ }x-1}\)-\(\dfrac{1}{\sqrt{x}+1}\)):(\(\dfrac{1}{\sqrt{x}+1}\)+\(\dfrac{2}{\sqrt{ }x-1}\)) với x>0,\(x\ne1\)

a, rút gọn P

tính P khi x=4-2\(\sqrt{3}\)

Answer 1

cho pt (\(\dfrac{\sqrt{x}}{\sqrt{ }x-1}\)-\(\dfrac{1}{\sqrt{x}+1}\)):(\(\dfrac{1}{\sqrt{x}+1}\)+\(\dfrac{2}{\sqrt{ }x-1}\)) với x>0,\(x\ne1\)

a, rút gọn P

tính P khi x=4-2\(\sqrt{3}\)

Answer 2

a: \(P=\dfrac{x+\sqrt{x}-\sqrt{x}+1}{x-1}:\dfrac{\sqrt{x}-1+2\sqrt{x}+2}{x-1}\)

\(=\dfrac{x+1}{3\sqrt{x}+1}\)

b: Khi \(x=4-2\sqrt{3}\) thì

\(P=\dfrac{4-2\sqrt{3}+1}{3\left(\sqrt{3}-1\right)+3}=\dfrac{5-2\sqrt{3}}{3\sqrt{3}}\)

Answer 3

giải rõ với ạ em là hs

Answer 4

a.P=\(\left(\dfrac{\sqrt{x}.\left(\sqrt{x}+1\right)}{x-1}-\dfrac{\sqrt{x-1}}{x-1}\right):\left(\dfrac{\sqrt{x}-1}{x-1}+\dfrac{2.\left(\sqrt{x}+1\right)}{x-1}\right)\)

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

=\(\dfrac{x+1}{x-1}:\dfrac{3\sqrt{x}+1}{x-1}\)

=\(\dfrac{x+1}{x-1}.\dfrac{x-1}{3\sqrt{x}+1}\)

=\(\dfrac{x+1}{3\sqrt{x}+1}\)