Violympic toán 9
Các câu hỏi tương tự
\(P=\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}+\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)\left(\frac{\sqrt{x}+1}{\sqrt{x-1}}+\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)-2\sqrt{x}\)
rút gọn P
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 \(x=\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{13}}}+\sqrt{27-10\sqrt{2}}\)\(A=\frac{\sqrt{x}+1}{3\left(\sqrt{x}-1\right)}\)
Rút gọn \(M=\left(\frac{2x+3\sqrt{x}}{2\sqrt{x}+1}+\frac{1}{x-\sqrt{x}+1}-\frac{1}{\sqrt{x}+1}\right).\left(\frac{x-\sqrt{x}+1}{\sqrt{x}}\right)\)
Rút gọn:
\(\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}—2}-\frac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)
1. Rút gọn
P=\(2\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}:\left[\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}-\frac{1}{2}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2\right]\)
LARGE 7)Gfrac{sqrt{x}+1}{x-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2sqrt{x}+2}{x-1}Gfrac{sqrt{x}+1}{sqrt{x}-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2(sqrt{x}+1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{sqrt{x}+1}{x-1}+frac{sqrt{x}-1}{sqrt{x}+1}-frac{2}{sqrt{x}-1}Gfrac{(sqrt{x}+1)^2+(sqrt{x}-1)^2-2(sqrt{x}+1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2x-2sqrt{x}}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2sqrt{x}(sqrt{x}-1)}{(sqrt{x}-1)(sqrt{x}+1)}Gfrac{2sqrt{x}}{sqrt{x}+1}8)H(frac{1}{sqrt{x}-1}+frac{sqrt{x}}{x-1}):(frac{sqrt{x}}{sqrt{x}-1}-...
Đọc tiếp
\[\LARGE 7)G=\frac{\sqrt{x}+1}{x-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2\sqrt{x}+2}{x-1}\\G=\frac{\sqrt{x}+1}{\sqrt{x}-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{\sqrt{x}+1}{x-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{2}{\sqrt{x}-1}\\G=\frac{(\sqrt{x}+1)^2+(\sqrt{x}-1)^2-2(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2x-2\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2\sqrt{x}(\sqrt{x}-1)}{(\sqrt{x}-1)(\sqrt{x}+1)}\\G=\frac{2\sqrt{x}}{\sqrt{x}+1}\\8)H=(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}):(\frac{\sqrt{x}}{\sqrt{x}-1}-1)\\H=(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}):(\frac{\sqrt{x}-(\sqrt{x}-1)}{\sqrt{x}-1})\\H=\frac{\sqrt{x}+1+\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}:\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}-1}\\H=\frac{2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}:\frac{1}{\sqrt{x}-1}\\H=\frac{2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}.(\sqrt{x}-1)\\H=\frac{2\sqrt{x}}{\sqrt{x}+1}\]
CHO P = \(\left(\frac{2x\sqrt{x}+x-\sqrt{x}}{x\sqrt{x}-1}-\frac{x+\sqrt{x}}{x-1}\right)\frac{x-1}{2x+\sqrt{x}-1}+\frac{\sqrt{x}}{2\sqrt{x}-1}\)
a. rút gọn P
rút gọn:
B=\(1+\left(\frac{2x+\sqrt{x}-1}{1-x}-\frac{2x\sqrt{x}-\sqrt{x}+x}{1-x\sqrt{x}}\right).\frac{x-\sqrt{x}}{2\sqrt{x}-1}\)
Rút gọn :\(A=\frac{2x+2}{\sqrt{x}}+\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}\)
Rút gọn \(B=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\left(x-1\right)}{\sqrt{x}-1}\)