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Bài 8: Rút gọn biểu thức chứa căn bậc hai
Các câu hỏi tương tự
Rút gọn biểu thức:
a, \(\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\dfrac{3\sqrt{x}-2}{1-\sqrt{x}}-\dfrac{2\sqrt{x}+3}{3+\sqrt{x}}\)
b, \(\dfrac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-\dfrac{2a+\sqrt{a}}{\sqrt{a}}+1\)
Adfrac{sqrt{x}+2}{sqrt{x}-2}-dfrac{3}{sqrt{x}+2}+dfrac{12}{x-4}Bdfrac{sqrt{x}}{sqrt{x}-3}-dfrac{sqrt{x}-21}{9-x}dfrac{1}{sqrt{x}+3}Cdfrac{sqrt{x}}{sqrt{x}+3}+dfrac{2sqrt{x}}{sqrt{x}-3}-dfrac{3x+9}{x-9}Ddfrac{1}{sqrt{x}+3}-dfrac{sqrt{x}}{3-sqrt{x}}+dfrac{2sqrt{x}+12}{x-9}Ndfrac{sqrt{x}}{sqrt{x}-1}+dfrac{2sqrt{x}-1}{sqrt{x}+1}-dfrac{6}{x-1}Mdfrac{3}{sqrt{x}-3}+dfrac{2}{sqrt{x}+3}+dfrac{x-5sqrt{x}-3}{x-9}
Đọc tiếp
\(A=\dfrac{\sqrt{x}+2}{\sqrt{x}-2}-\dfrac{3}{\sqrt{x}+2}+\dfrac{12}{x-4}\)
\(B=\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{\sqrt{x}-21}{9-x}\dfrac{1}{\sqrt{x}+3}\)
\(C=\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+9}{x-9}\)
\(D=\dfrac{1}{\sqrt{x}+3}-\dfrac{\sqrt{x}}{3-\sqrt{x}}+\dfrac{2\sqrt{x}+12}{x-9}\)
\(N=\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{6}{x-1}\)
\(M=\dfrac{3}{\sqrt{x}-3}+\dfrac{2}{\sqrt{x}+3}+\dfrac{x-5\sqrt{x}-3}{x-9}\)
chứng minh rằng
a, \(\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}=1\)
b, \(\frac{1}{x+\sqrt{x}}+\frac{2\sqrt{x}}{x-1}-\frac{1}{x-\sqrt{x}}=\frac{2}{\sqrt[]{x}}\)
Rút gọn:
A=\(\left(\dfrac{x-\sqrt{x}+2}{x-\sqrt{x}-2}-\dfrac{x}{x-2\sqrt{x}}\right)\div\dfrac{1-\sqrt{x}}{2-\sqrt{x}}vớix>0,x\ne1\)
B=\(\left(\dfrac{x}{3+\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right)\div\left(1-\dfrac{2}{\sqrt{x}}+\dfrac{6}{x+3\sqrt{x}}\right)\)
Lm nhanh giúp mk nhé!
Cho \(P=\left(\dfrac{x-1}{3+\sqrt{x-1}}+\dfrac{x+8}{10-x}\right):\left(\dfrac{3\sqrt{x-1}+1}{x-3\sqrt{x-1}-1}-\dfrac{1}{\sqrt{x-1}}\right)\)
a) Rút gọn .
b) Tính giá trị P khi \(x=\sqrt{\dfrac{3+2\sqrt{2}}{3-2\sqrt{2}}}-\sqrt{\dfrac{3-2\sqrt{2}}{3+2\sqrt{2}}}\)
C=\([1-\dfrac{\sqrt{x}}{1+\sqrt{x}}][\dfrac{\sqrt{x}+3}{\sqrt{x}-2}+\dfrac{2+\sqrt{x}}{3-\sqrt{x}}+\dfrac{\sqrt{x}+2}{x-5\sqrt{x}+6}1]\)
cho biểu thức P=\(\left(\dfrac{1}{\sqrt{x}-\sqrt{x-1}}-\dfrac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\dfrac{2}{\sqrt{2}-\sqrt{x}}-\dfrac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
a,rút gọn biểu thức
b,tính giá trị của biểu thức với x=3 - \(2\sqrt{2}\)
Rút gọn biểu thức
a,frac{1}{left(2sqrt{x}-2right)}-frac{1}{left(2sqrt{x}+2right)}+frac{sqrt{x}}{left(1-xright)}
b, left(dfrac{sqrt{x}-sqrt{y}}{1+sqrt{xy}}+dfrac{sqrt{x}+sqrt{y}}{1-sqrt{xy}}right):left(dfrac{x+y+2xy}{1-xy}+1right)
c, dfrac{3left(x+sqrt{x}-3right)}{x+sqrt{x}-2}+dfrac{sqrt{x}+3}{sqrt{x}+2}-dfrac{sqrt{x}-2}{sqrt{x}-1}
Đọc tiếp
Rút gọn biểu thức
a,\(\frac{1}{\left(2\sqrt{x}-2\right)}-\frac{1}{\left(2\sqrt{x}+2\right)}+\frac{\sqrt{x}}{\left(1-x\right)}\)
b, \(\left(\dfrac{\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}+\dfrac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}\right):\left(\dfrac{x+y+2xy}{1-xy}+1\right)\)
c, \(\dfrac{3\left(x+\sqrt{x}-3\right)}{x+\sqrt{x}-2}+\dfrac{\sqrt{x}+3}{\sqrt{x}+2}-\dfrac{\sqrt{x}-2}{\sqrt{x}-1}\)
1) \(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}}\)
2)\(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{2+5\sqrt{x}}{4-x}\)
\(A= (\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+3}{x-9}):(\dfrac{2\sqrt{x}-2}{\sqrt{x}-3}-1)\)
a) Rút gọn A
b) Tìm x khi A=1