Các câu hỏi tương tự
\(A=\left(\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)
a Rút gọn biểu thức
b Tính giá trị của \(\sqrt{A}\) khi x=\(4+2\sqrt{3}\)
\(F=\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{2\sqrt{x}+7}{x-4}\right):\left(\frac{3-\sqrt{x}}{\sqrt{x}-2}+1\right)\)
a,rút gọn
b,tính F biết x=9-\(4\sqrt{5}\)
c, tìm GTNN của F
\(A=\frac{\sqrt{x}-2}{\sqrt{x}-1}vaB=\left(\frac{\sqrt{x}}{\sqrt{x}+1}+\frac{1}{\sqrt{x}-1}\right).\frac{\sqrt{x}-1}{x+1}\left(x\ge0,x\ne1\right)\)
a Tính giá trị biểu thức A khi x=9
b Rút gọn B
c Đặt P=B:(A-1)
Cho P= \(\left(1-\frac{\sqrt{3}}{x-9}+\frac{3}{\sqrt{x}-3}\right):\frac{\sqrt{x}}{\sqrt{x}+3}\)
a, Rút gọn biểu thức P
b, Tính giá trị P khi x=\(11+6\sqrt{2}\)
c, Tìm x để P nguyên
giúp tớ
Cho P=\(\left(1-\frac{\sqrt{3}}{x-9}+\frac{3}{\sqrt{x}-3}\right):\frac{\sqrt{x}}{\sqrt{x}+3}\)
a, rút gọn P
b,tính giá trị P khi x=\(11+6\sqrt{2}\)
c,tìm x để P nguyên
Cho biểu thức : \(A=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\).
a) Rút gọn A .
b) Cho \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=6\). Tính giá trị lớn nhất của A .
Rút gọn: \(A=\frac{\sqrt{1+\sqrt{1-x^2}}.\left[\sqrt{\left(1+x\right)^3}-\sqrt{\left(1-x\right)^3}\right]}{2+\sqrt{1-x^2}}\)
Giải giúp mk... Mk cần gấp.
1.tính giá trị biểu thức \(A=\frac{1-ax}{1+ã}\sqrt{\frac{1+bx}{1-bx}}\)với \(x=\frac{1}{a}\sqrt{\frac{2a}{b}-1}\left(0< a< b< 2a\right)\)
2. cho \(M=\sqrt{\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{x^2+\sqrt{x}}{x-\sqrt{x}+1}+x+1}\).rút gọn M vs \(0\le x\le1\)
Bleft(frac{xsqrt{x}+x+sqrt{x}}{xsqrt{x}-1}-frac{sqrt{x}+3}{1-sqrt{x}}right).frac{x-1}{2x+sqrt{x}-1} ĐKXĐ: ...frac{left(xsqrt{x}+x+sqrt{x}right)left(1-sqrt{x}right)-left(sqrt{x}+3right)left(xsqrt{x}-1right)}{left(xsqrt{x}-1right)left(1-sqrt{x}right)}.frac{x-1}{2x+2sqrt{x}-sqrt{x}-1}frac{xsqrt{x}+x+sqrt{x}-x^2-xsqrt{x}-x-x^2+sqrt{x}-3xsqrt{x}+3}{left(xsqrt{x}-1right)left(1-sqrt{x}right)}.frac{x-1}{2sqrt{x}left(sqrt{x}+1right)-left(sqrt{x}+1right)}frac{-3xsqrt{x}+2sqrt{x}-2x^2+3}{left(xsqrt{x}-1ri...
Đọc tiếp
\(B=\left(\frac{x\sqrt{x}+x+\sqrt{x}}{x\sqrt{x}-1}-\frac{\sqrt{x}+3}{1-\sqrt{x}}\right).\frac{x-1}{2x+\sqrt{x}-1}\) ĐKXĐ: ...
\(=\frac{\left(x\sqrt{x}+x+\sqrt{x}\right)\left(1-\sqrt{x}\right)-\left(\sqrt{x}+3\right)\left(x\sqrt{x}-1\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{2x+2\sqrt{x}-\sqrt{x}-1}\)
\(=\frac{x\sqrt{x}+x+\sqrt{x}-x^2-x\sqrt{x}-x-x^2+\sqrt{x}-3x\sqrt{x}+3}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{2\sqrt{x}\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)}\)
\(=\frac{-3x\sqrt{x}+2\sqrt{x}-2x^2+3}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{3-3x\sqrt{x}+2\sqrt{x}-2x^2}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{3\left(1-x\sqrt{x}\right)+2\sqrt{x}\left(1-x\sqrt{x}\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{\left(2\sqrt{x}+3\right)\left(1-x\sqrt{x}\right)}{\left(x\sqrt{x}-1\right)\left(1-\sqrt{x}\right)}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{-2\sqrt{x}-3}{1-\sqrt{x}}.\frac{x-1}{\left(2\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\frac{-2\sqrt{x}-3}{1-\sqrt{x}}.\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{2\sqrt{x}-1}\)
\(=\frac{2\sqrt{x}+3}{2\sqrt{x}-1}\)