a) ĐKXĐ : x\(\ne\)1
rút gọn
B =( \(\dfrac{1}{x-\sqrt{x}}\)+\(\dfrac{1}{\sqrt{x-1}}\)) : \(\dfrac{\sqrt{x}-1}{\left(\sqrt{x-1}\right)^2}\)
B=( \(\dfrac{1}{\sqrt{x}\left(\sqrt{x-1}\right)}\)+\(\dfrac{1}{\sqrt{x-1}}\)) : \(\dfrac{1}{\sqrt{x-1}}\)
B= \(\dfrac{1+\sqrt{x}}{\sqrt{x}\left(\sqrt{x-1}\right)}\).\(\dfrac{\sqrt{x-1}}{1}\)
B= \(\dfrac{1+\sqrt{x}}{\sqrt{x}}\)
Cho B=
\(\dfrac{1}{X-\sqrt{X}}\)+\(\dfrac{1}{\sqrt{X}-1}\):\(\dfrac{\sqrt{X}-1}{\left(\sqrt{X}-1\right)^2}\)
a,rút gọn và tìm ĐkXĐ
b,tìm B khi x= 3+2\(\sqrt{3}\)
c,tìm min P= B×(x-2\(\sqrt{X}\))
Cho M= \(\left(1-\dfrac{x-3\sqrt{x}}{x-9}\right):\left(\dfrac{9-x}{x+\sqrt{x}-6}-\dfrac{\sqrt{x}-3}{2-\sqrt{x}}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)
a) Rút gọn M
b) Tìm các giá trị của x để có \(\dfrac{5}{3}M\) = \(\sqrt{x}+4\)
Tìm Min và Max(nếu có)
A=2x-\(\sqrt{x}\)
B=x+\(\sqrt{x}\)
C=1+\(\sqrt{2-x}\)
D=\(\sqrt{-x^2+2x+5}\)
E=\(\dfrac{1}{2x-\sqrt{x}+3}\)
F=\(\dfrac{1}{3-\sqrt{1-x^2}}\)
rút gọn
B=\(\dfrac{x\sqrt{x}-8}{x-2\sqrt{x}}-\dfrac{x\sqrt{x}+8}{x+2\sqrt{x}}+\dfrac{x+2}{\sqrt{x}}\)tìm đk để B rút gọn
C=\(\dfrac{1}{\sqrt{x}+2}-\dfrac{5}{x-\sqrt{x}-6}-\dfrac{\sqrt{x}-2}{3-\sqrt{x}}\)tìm x ∈Z để C ∈Z
B=\(\left(\dfrac{3}{\sqrt{1+a}}+\sqrt{1-a}\right):\left(\dfrac{3}{\sqrt{1-a^2}}+1\right)\)
a) Rút gọn
b) Tìm B khi a=\(\dfrac{\sqrt{3}}{2+\sqrt{3}}\)
c) Tìm a để \(\sqrt{B}>B\)
\(C=\dfrac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left(\dfrac{1}{x}+\dfrac{1}{y}\right).\dfrac{1}{x+y+2\sqrt{xy}}+\dfrac{2}{\left(\sqrt{x}+\sqrt{y}\right)^3}.\left(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}\right)\)
a) Rút gọn
b) Tính C với x=2-\(\sqrt{3}\); y=2+\(\sqrt{3}\)
Rút gọn biểu thức
\(a.\dfrac{\sqrt{5}-2\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\dfrac{2\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)
\(b.x\sqrt{2x+2}+\left(x+1\right)\sqrt{\dfrac{2}{x+1}}-4\sqrt{\dfrac{x+1}{2}}\)
Bài 1: Tính:
\(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
Bài 2: Rút gọn rồi tính:
a) A=\(\dfrac{a^4-4a^2+3}{a^4-12a^2+27},a=\sqrt{3}-\sqrt{2}\)
b) \(B=\dfrac{1}{\sqrt{h+2\sqrt{h-1}}}+\dfrac{1}{\sqrt{h-2\sqrt{h-1}}},h=3\)
c) \(C=\dfrac{\sqrt{2x+2\sqrt{x^2-4}}}{\sqrt{x^2-4}x+2},x=2\left(\sqrt{3}+1\right)\)
d) \(D=\left(\dfrac{3}{\sqrt{1+a}}+\sqrt{1-a}\right):\left(\dfrac{3}{\sqrt{1-a^2}}+1\right),a=\dfrac{\sqrt{3}}{2+\sqrt{3}}\)
Mọi người giúp em với!!!!!!!!!!!!!!
Bải 1 :Rút gọn :
\(M=\left(\dfrac{2+\sqrt{x}}{x+2\sqrt{x}+1}-\dfrac{\sqrt{x}-2}{x-1}\right)\)\(\left(\dfrac{x\sqrt{x}+x-\sqrt{x}-1}{\sqrt{x}}\right)\)
Bài 2 : Rút gọn :
\(P=\left(1+\dfrac{\sqrt{x}}{x+1}\right):\)\(\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}\right)\)
