`\sqrt{[27(x-1)^2]/12} +3/2 - (x - 2)\sqrt{[50x^2]/[8(x-2)^2]}` `(1 < x < 2)`
`=\sqrt{[3(x-1)]^2 .3}/\sqrt{2^2 .3} + 3/2 - (x - 2) \sqrt{(5x)^2 . 2}/\sqrt{[2(x - 2)]^2 . 2}`
`=[3\sqrt{3}|x-1|]/[2\sqrt{3}]+3/2-(x-2)[5\sqrt{2}|x|]/[2\sqrt{2}|x-2|]`
`=[3(x-1)]/2+3/2-[5x(x-2)]/[2(2-x)]` (Vì `1 < x < 2`)
`=3/2x - 3/2 + 3/2 + 5/2x`
`=4x`
\(B=\dfrac{x^3-3x+\left(x^2-1\right)\sqrt{x^2-4}-2}{x^3-3x+\left(x^2-1\right)\sqrt{x^2-4}+2}\)với x > 0 rút gọn biểu thức ( cho em xin lời giải chi tiết ạ )
rút gọn hoạc tính giá trị các biểu thức sau
1)1+\(\sqrt{\dfrac{\left(x-1\right)^2}{x-1}}\)
2)\(\sqrt{\left(x-2\right)^2}+\dfrac{x-2}{\sqrt{\left(x-2\right)^2}}\)
3)\(\sqrt{m}-\sqrt{m-2\sqrt{m}+1}\)
Cho P =\(\left(\dfrac{3\sqrt{x}+x+2}{\left(\sqrt{x}+2\right).\left(\sqrt{x}+1\right)}-\dfrac{x+\sqrt{x}}{x-1}\right):\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\right)\)
a) Tìm ĐKXĐ, rút gọn
b) Tìm x khi P=-4
c) Tìm P khi x =\(8-2\sqrt{15}\)
Cho P \(=\left(\dfrac{3\sqrt{x}+x+2}{\left(\sqrt{x+2}\right).\left(\sqrt{x}-1\right)}\dfrac{x+\sqrt{x}}{x-1}\right):\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\right)\)
a) Tìm ĐKXĐ, rút gọn
b) Tìm x khi P=-4
c) Tìm P khi x =\(8-2\sqrt{15}\)
bài 1 : rút gọn các biểu thức sau .
a, \(\sqrt{4\left(a-3\right)^2}+2\sqrt{a^2+4a+4}\left(a< -2\right)\)
b, \(\sqrt{\dfrac{\left(x-2\right)^2}{\left(3-2\right)^2}}+\dfrac{x^2-1}{x-3}\left(x< 3\right)\)
c, \(4x-\sqrt{8}+\dfrac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}\)
bài 2 thực hiện phép tính :\
a, \(\sqrt{8-\sqrt[2]{7}}\times\sqrt{8+\sqrt[2]{7}}\)
b, \(\sqrt{4+\sqrt{8}+}+\sqrt{2}+\sqrt{2+\sqrt{2}}\times\sqrt{2-\sqrt{2+2}}\)
c, \(\left(4+\sqrt{15}\right)\times\sqrt{10}-\sqrt{6}\times\sqrt{4-\sqrt{15}}\)
d, \(\left(2+\sqrt{3}\right)^2-\left(2-\sqrt{3}\right)\times\left(2+\sqrt{3}\right)\)
BÀI 1 : THỰC HIỆN PHÉP TÍNH
a, \(\left(1+\sqrt{3}-\sqrt[2]{2}\right)\times\left(1+\sqrt{3}+\sqrt[2]{2}\right)\)
b, \(\left(\dfrac{3}{2}\times\sqrt{6}+2\times\sqrt{\dfrac{2}{3}}-4\times\sqrt{\dfrac{3}{2}}\right)\times\left(3\times\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)
BÀI 2 : rút gọn
B = \(\sqrt{x+2\sqrt{2x-4}}+\sqrt{x-2\sqrt{2x-2}}\)
Rút gọn biểu thức:
a) \(\dfrac{x\sqrt{x}+y\sqrt{y}}{\sqrt{x}+\sqrt{y}}-\left(\sqrt{x}-\sqrt{y}\right)^2\);
b) \(\sqrt{\dfrac{x-2\sqrt{x}+1}{x+2\sqrt{x}+1}}\) (\(x\ge0\))
c)\(\dfrac{x-1}{\sqrt{y}-1}\cdot\sqrt{\dfrac{\left(y-2\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}\) (\(x\ne1\), \(y\ne1\), \(y>0\)).
Cho E= \(\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}-\dfrac{1}{x-\sqrt{x}}\right):\left(\dfrac{1}{\sqrt{x}+1}+\dfrac{2}{x-1}\right)\)
a) ĐKXĐ E
b) Rút gọn
Cho \(Q=\left(\dfrac{1}{\sqrt{x}-2}+\dfrac{5\sqrt{x}-4}{2\sqrt{x}-x}\right):\left(\dfrac{2+\sqrt{x}}{\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)\)
a) Tìm ĐKXĐ và Rút gọn
b) Tìm x khi Q =5
c) Tìm Q khi x=\(\dfrac{3-\sqrt{5}}{2}\)
