a: \(P=\left(\dfrac{x-1}{2\sqrt{x}}\right)^2\cdot\dfrac{x-2\sqrt{x}+1-x-2\sqrt{x}-1}{x-1}\)
\(=\dfrac{\left(x-1\right)^2}{4x}\cdot\dfrac{-4\sqrt{x}}{x-1}=\dfrac{-\left(x-1\right)}{\sqrt{x}}\)
b: Khi \(x=4+2\sqrt{3}\) thì \(P=\dfrac{-\left(4+2\sqrt{3}-1\right)}{\sqrt{3}+1}=\dfrac{-\left(3+2\sqrt{3}\right)}{\sqrt{3}+1}=\dfrac{-3-\sqrt{3}}{2}\)
c: Để P<0 thì -(x-1)<0
=>x-1>0
=>x>1
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 \(\dfrac{5}{3}M\) = \(\sqrt{x}+4\)
Rút gọn biểu thức
\(a.\dfrac{\sqrt{5}-2\sqrt{3}}{\sqrt{5}+\sqrt{3}}-\dfrac{2\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\)
\(b.x\sqrt{2x+2}+\left(x+1\right)\sqrt{\dfrac{2}{x+1}}-4\sqrt{\dfrac{x+1}{2}}\)
\(C=\dfrac{\sqrt{x}-\sqrt{y}}{xy\sqrt{xy}}:\left(\dfrac{1}{x}+\dfrac{1}{y}\right).\dfrac{1}{x+y+2\sqrt{xy}}+\dfrac{2}{\left(\sqrt{x}+\sqrt{y}\right)^3}.\left(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}\right)\)
a) Rút gọn
b) Tính C với x=2-\(\sqrt{3}\); y=2+\(\sqrt{3}\)
Rút gọn
a. \(\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{x^2+x}{x-\sqrt{x}+1}+x+1\) với x > 0
b. \(\left(\dfrac{2+\sqrt{x}}{x+2\sqrt{x}+1}-\dfrac{\sqrt{x}-2}{x-1}\right)\left(\dfrac{x\sqrt{x}+x-\sqrt{x}-1}{\sqrt{x}}\right)\) với x > 0
rút gọn
A=\(\dfrac{8+x\left(1+\sqrt{x-2\sqrt{x}+1}\right)}{\left(x-4\right)\left(x-2\sqrt{x}+4\right)}+\dfrac{x-3\sqrt{x}}{2\left(x-\sqrt{x}-6\right)}\)
lm nhanh giúp mk nhé
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 :
\(P=\left(1+\dfrac{\sqrt{x}}{x+1}\right):\)\(\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2\sqrt{x}}{x\sqrt{x}+\sqrt{x}-x-1}\right)\)
Bài 1 Cho biểu thức
a) H = \(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{2\sqrt{x}-1}{x-\sqrt{x}}\)
1 Rút gọn H
2 Tìm x để H < 0
b) Q = \(\left(\dfrac{x+\sqrt{x}}{\sqrt{x}+1}+1\right):\left(\dfrac{x-\sqrt{x}}{\sqrt{x}-1}-1\right)\)
1 Rút gọn Q
2 Tìm x để Q < 1
GIÚP MÌNH VS CẦN GẤP LẮM NHA !!!!!!
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!!!!!!!!!!!!!!
cho A=\(\left(\dfrac{\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+2+4\sqrt{x-2}}}{\sqrt{\dfrac{4}{x^2}}-\sqrt{\dfrac{4}{x}}+1}\right)\)với x>8
a)rút gọn A
b)tìm x nguyên để A có giá trị nguyên
