Rút gọn B
\(B=\frac{2\left(x+4\right)}{x-3\sqrt{x}-4}+\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{8}{\sqrt{x}-4}\)
Rút gọn
a) \(\left(\frac{2+\sqrt{a}}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}\right)\left(\frac{a\sqrt{a}-\sqrt{a}-1}{\sqrt{a}}\right)\)
b) \(\left(\frac{\sqrt{x}+1}{x-4}-\frac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right)\left(\frac{x\sqrt{x}+2x+4\sqrt{x}-8}{\sqrt{x}}\right)\)
A=\(\left(\frac{3\sqrt{x}}{\sqrt{x}+2}-\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{8\sqrt{x}}{x-4}\right):\left(2-\frac{2\sqrt{x}+3}{\sqrt{x}+2}\right)\left(x\ge0,x\ne4\right)\)
a, Rút gọn A.
b, Tìm GTNN của A khi x>4
\(A=\frac{3\sqrt{x}\left(\sqrt{x}-2\right)-\sqrt{x}\left(\sqrt{x}+2\right)+8\sqrt{x}}{x-4}:\frac{2\left(\sqrt{x}+2\right)-2\sqrt{x}-3}{\sqrt{x}+2}\)
\(A=\frac{2x}{x-4}.\left(\sqrt{x}+2\right)=\frac{2x\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\)
\(A=\frac{2x}{\sqrt{x}-2}\)
\(B=\frac{2\left(x+4\right)}{x-3\sqrt{x}-4}+\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{8}{\sqrt{x}-4}\) \(ĐKXĐ:x\ge0;x\ne16\)
a) rút gọn B
\(B=\frac{2\left(x+4\right)}{x-3\sqrt{x}-4}+\frac{\sqrt{x}}{\sqrt{x}+1}-\frac{8}{\sqrt{x}-4}\)
\(B=\frac{2\left(x+4\right)+\sqrt{x}\left(\sqrt{x}-4\right)-8\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(B=\frac{2x+8+x-4\sqrt{x}-8\sqrt{x}-8}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(B=\frac{3x-12\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(B=\frac{3\sqrt{x}\left(\sqrt{x}-4\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-4\right)}\)
\(B=\frac{3\sqrt{x}}{\sqrt{x}+1}\)
vậy \(B=\frac{3\sqrt{x}}{\sqrt{x}+1}\)
Cho: \(P=\left(\frac{4\sqrt{x}}{2+\sqrt{x}}+\frac{8-x}{4-x}\right):\left(\frac{\sqrt{x}-1}{x-2\sqrt{x}}-\frac{2}{\sqrt{x}}\right)\)
a. Rút gọn
b. Với x > 9. Tìm m để \(m\left(\sqrt{x}-3\right).P>x+1\)
Rút gọn các biểu thức:
a, \(A=\frac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}-\frac{2+\sqrt{8}}{1+\sqrt{2}}\)
b, \(B=\left(\frac{1}{x-4}-\frac{1}{x+4\sqrt{x}+4}\right).\frac{x+2\sqrt{x}}{\sqrt{x}}\)(với x>0, x khác 4)
Cho biểu thức P=\(\left(\frac{\sqrt{x-1}}{3+\sqrt{x-1}}+\frac{x+8}{10-x}\right):\left(\frac{3\sqrt{x-1}+1}{x-3\sqrt{x-1}-1}-\frac{1}{\sqrt{x-1}}\right)\)
a) Rút gọn P
b) Tính giá trị của P khi \(x=\sqrt[4]{\frac{3+2\sqrt{2}}{3-2\sqrt{2}}}-\sqrt[4]{\frac{3-2\sqrt{2}}{3+2\sqrt{2}}}\)
cho biểu thức \(P=\left(\frac{\sqrt{x-1}}{3+\sqrt{x-1}}+\frac{x+8}{10-x}\right):\left(\frac{3\sqrt{x-1}+1}{x-3\sqrt{x-1}-1}-\frac{1}{\sqrt{x-1}}\right)\)
a) rút gọn
b) tính gt P khi \(x=\sqrt[4]{\frac{3+2\sqrt{2}}{3-2\sqrt{2}}}-\sqrt[4]{\frac{3-2\sqrt{2}}{3+2\sqrt{2}}}\)
a) ĐK: x > 1
\(P=\left(\frac{\sqrt{x-1}}{3+\sqrt{x-1}}+\frac{x+8}{9-\left(x-1\right)}\right):\left(\frac{3\sqrt{x-1}+1}{\left(x-1\right)-3\sqrt{x-1}}-\frac{1}{\sqrt{x-1}}\right)\)
\(P=\frac{\sqrt{x-1}\left(3-\sqrt{x-1}\right)+x+8}{9-\left(x-1\right)}:\frac{3\sqrt{x-1}+1-\left(\sqrt{x-1}-3\right)}{\sqrt{x-1}\left(\sqrt{x-1}-3\right)}\)
\(P=\frac{3\sqrt{x-1}-x+1+x+8}{10-x}:\frac{2\sqrt{x-1}+4}{\sqrt{x-1}\left(\sqrt{x-1}-3\right)}\)
\(P=\frac{3\left(\sqrt{x-1}+3\right)}{10-x}.\frac{\sqrt{x-1}\left(\sqrt{x-1}-3\right)}{2\sqrt{x-1}+4}\)
\(P=\frac{-3\sqrt{x-1}}{2\sqrt{x-1}+4}\)
b) \(x=\sqrt[4]{\frac{17+12\sqrt{2}}{1}}-\sqrt[4]{\frac{17-12\sqrt{2}}{1}}=1+\sqrt{2}-\left(\sqrt{2}-1\right)=2\)
Vậy \(P=\frac{-3\sqrt{2-1}}{2\sqrt{2-1}+4}=-\frac{1}{2}\)
cô Hoàng Thị Thu Huyền làm rõ cho em ý b đc ko ạ chỗ biến đổi x
tất cả phải nghe theo lệnh của cô chủ nhiệm tập đoàn của cô Hoàng Thị Thu Huyền&Trần Thị Loan nhưng hôm nay không cô Trần Thị Loan nên tôi thay mặt cho vì hai cô này có chức Quản Lý
Rút gọn B=\(\left(\frac{1}{\sqrt{x}-2}-\frac{2}{\sqrt{x}+2}+\frac{x}{x\sqrt{x}-4\sqrt{x}}\right):\left(\frac{6-x}{\sqrt{x}+2}+2+\sqrt{x}\right)\)
\(B=\left(\frac{1}{\sqrt{x}-2}-\frac{2}{\sqrt{x}+2}+\frac{x}{x\sqrt{x}-4\sqrt{x}}\right):\left(\frac{6-x}{\sqrt{x}+2}+2+\sqrt{x}\right)\)
\(B=\left(\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{2\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x+2}\right)}\right):\left(\frac{6-x+2\left(\sqrt{x}+2\right)+\sqrt{x}\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\right)\)
\(B=\left(\frac{\sqrt{x}+2-2\sqrt{x}+4+\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right):\left(\frac{6-x+2\sqrt{x}+4+x+2\sqrt{x}}{\sqrt{x}+2}\right)\)
\(B=\frac{6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\frac{\sqrt{x}+2}{10+4\sqrt{x}}\)
\(B=\frac{6}{\sqrt{x}-2}\cdot\frac{1}{2\left(5+2\sqrt{x}\right)}\)
B = \(\frac{3}{\left(\sqrt{x}-2\right)\left(5+2\sqrt{x}\right)}\)
Cho B=\(\left(\frac{x-\sqrt{x}+7}{x-4}+\frac{1}{\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}-2}-\frac{\sqrt{x}-2}{\sqrt{x}+2}-\frac{2\sqrt{x}}{x-4}\right)\)
a) Rút gọn
b) So sánh B và \(\frac{1}{B}\)
Rút gọn A = \(\left(\frac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\frac{x+2\sqrt{x}+1}{x-1}\right) :\left(3+\frac{1}{\sqrt{x}-2}+\frac{2}{\sqrt{x}+1}\right)\)
a, Rút gọn A b , Tìm x thỏa mãn A > 1 c,Tính A với \(x=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)\(A=\frac{\sqrt{x}+1}{3\left(\sqrt{x}-1\right)}\)