rút gọn \(M=\frac{a+1}{\sqrt{a}}+\frac{a\sqrt{a}-1}{a-\sqrt{a}}+\frac{a^2-a\sqrt{a}+\sqrt{a}+1}{\sqrt{a}-a\sqrt{a}}\)
Những câu hỏi liên quan
rút gọn biểu thức \(\frac{a\sqrt{a}-1}{a-\sqrt{a}}-\frac{a\sqrt{a+1}}{\sqrt{a}}+\left(\sqrt{a-}\frac{1}{\sqrt{a}}\right).\left(\frac{3\sqrt{a}}{\sqrt{a-1}}-\frac{2+\sqrt{a}}{\sqrt{a+1}}\right)\)
Rút gọn các biểu thức
\(A=\left(1+\frac{\sqrt{a}-1}{a-\sqrt{a}}\right):\left(\frac{a+\sqrt{a}}{a-1}\frac{\sqrt{a}}{a-\sqrt{a}}\right)\)
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\)
\(C=\left(\frac{\sqrt{a}}{\sqrt{a}+1}-\frac{\sqrt{a}}{\sqrt{a}-1}+\frac{1}{a-1}\right):\frac{a}{2+2\sqrt{a}}\)
Rút gọn biểu thức:
\(A=\frac{a\sqrt{a}-1}{a-\sqrt{a}}-\frac{a\sqrt{a}+1}{a+\sqrt{a}}+\left[\sqrt{a}-\frac{1}{\sqrt{a}}\right]\left[\frac{\sqrt{a}+1}{\sqrt{a}-1}+\frac{\sqrt{a}-1}{\sqrt{a}+1}\right]\)
Điều kiện : a> 0 ; a khác 1
\(A=\frac{\left(\sqrt{a}\right)^3-1}{\sqrt{a}\left(\sqrt{a}-1\right)}-\frac{\left(\sqrt{a}\right)^3+1}{\sqrt{a}\left(\sqrt{a}+1\right)}+\left(\frac{a-1}{\sqrt{a}}\right)\left(\frac{\left(\sqrt{a}+1\right)^2+\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)
\(A=\frac{a+\sqrt{a}+1}{\sqrt{a}}-\frac{a-\sqrt{a}+1}{\sqrt{a}}+\left(\frac{a-1}{\sqrt{a}}\right)\left(\frac{2a+2}{a-1}\right)\)
\(A=\frac{2\sqrt{a}}{\sqrt{a}}+\frac{2\left(a+1\right)}{\sqrt{a}}=2+\frac{2\sqrt{a}\left(a+1\right)}{a}\)
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Rút gọn (ĐKXĐ)
\(A=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\)
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}+1}-\frac{\sqrt{a}}{\sqrt{a}-1}+\frac{1}{a-1}\right):\frac{a}{2+2\sqrt{a}}\)
\(A=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\left(a>0;a\ne1\right)\)
\(A=\frac{\sqrt{a}.\sqrt{a}-1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{\left(\sqrt{a}-1\right)+2}{a-1}\)
\(A=\frac{a-1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{\sqrt{a}+1}{a-1}\)
\(A=\frac{\sqrt{a}+1}{\sqrt{a}}:\frac{1}{\sqrt{a}-1}\)
\(A=\frac{\sqrt{a}+1}{\sqrt{a}}.\left(\sqrt{a}-1\right)=\frac{a-1}{\sqrt{a}}\)
Vậy..............
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}+1}-\frac{\sqrt{a}}{\sqrt{a}-1}+\frac{1}{a-1}\right):\frac{a}{2+2\sqrt{a}}\)( điều kiện như trên )
\(B=\frac{\sqrt{a}\left(\sqrt{a}-1\right)-\sqrt{a}\left(\sqrt{a}+1\right)+1}{a-1}:\frac{a}{2\left(1+\sqrt{a}\right)}\)
\(B=\frac{a-\sqrt{a}-a-\sqrt{a}+1}{a-1}:\frac{a}{\left(\sqrt{a}+1\right).2}\)
\(B=\frac{1-2\sqrt{a}}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}.\frac{\left(\sqrt{a}+1\right).2}{a}\)
\(B=\frac{2\left(1-2\sqrt{a}\right)}{a\left(\sqrt{a}-1\right)}\)
Vậy.........
_Minh ngụy_
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1) Afrac{asqrt{a}-1}{a-sqrt{a}}-frac{asqrt{a}+1}{a+sqrt{a}}+left(sqrt{a}-frac{1}{sqrt{a}}right)left(frac{sqrt{a}+1}{sqrt{a}-1}+frac{sqrt{a}-1}{sqrt{a}+1}right)a. Rút gọn A b. Tìm a để A7 c. Tìm a để A62) Afrac{15sqrt{x}-11}{x+2sqrt{x}-3}+frac{3sqrt{x}-2}{1-sqrt{x}}-frac{2sqrt{x}+3}{3+sqrt{x}}a. Rút gọn A b. tìm x để A03)Afrac{a^2+sqrt{a}}{a-sqrt{a}+1}-frac{2a+sqrt{a}}{sqrt{a}}+1a. Rút gọn A b. Tìm a để A2 c. Tìm giá trị nhỏ nhất của AGIÚP MÌNH ĐI MẤY PẠN...
Đọc tiếp
1) A=\(\frac{a\sqrt{a}-1}{a-\sqrt{a}}-\frac{a\sqrt{a}+1}{a+\sqrt{a}}+\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}+\frac{\sqrt{a}-1}{\sqrt{a}+1}\right)\)
a. Rút gọn A b. Tìm a để A=7 c. Tìm a để A>6
2) A=\(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}+\frac{3\sqrt{x}-2}{1-\sqrt{x}}-\frac{2\sqrt{x}+3}{3+\sqrt{x}}\)
a. Rút gọn A b. tìm x để A<0
3)\(A=\frac{a^2+\sqrt{a}}{a-\sqrt{a}+1}-\frac{2a+\sqrt{a}}{\sqrt{a}}+1\)
a. Rút gọn A b. Tìm a để A=2 c. Tìm giá trị nhỏ nhất của A
GIÚP MÌNH ĐI MẤY PẠN !!! THKS NHÌU
Bạn có thể đăng từng bài k như thế nhìn đã sợ ai làm
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1)đặt nhân tử chung quy đồng là xong
2)phân tích x+2cănx-3=(1-cănx)(3+cănx)
3)2a+căn a đặt căn a ra r rút gọn
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Rút gọn biểu thức:
A= \(\frac{a\sqrt{a}-1}{a-\sqrt{a}}-\frac{a\sqrt{a}+1}{â+\sqrt{a}}+\left[\sqrt{a}-\frac{1}{\sqrt{a}}\right]\left[\frac{\sqrt{a}+1}{\sqrt{a}-1}+\frac{\sqrt{a}-1}{\sqrt{a}+1}\right]\)
BT rút gọn với ĐK: a>0 và a khác 1:
M = \(\left(\frac{2+\sqrt{a}}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}\right)\)\(\frac{a\sqrt{a}+a-\sqrt{a}-1}{\sqrt{a}}\)
N = \(\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}-\frac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\)\(\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\)
\(M=\left(\frac{2+\sqrt{a}}{\left(\sqrt{a}+1\right)^2}-\frac{\sqrt{a}-2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\frac{a\left(\sqrt{a}+1\right)-\left(\sqrt{a}+1\right)}{a}\)
\(=\frac{\left(2+\sqrt{a}\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}-2\right)\left(\sqrt{a}+1\right)}{\left(\sqrt{a}+1\right)^2\left(\sqrt{a}-1\right)}\cdot\frac{\left(\sqrt{a}-1\right)\left(a-1\right)}{a}\)
\(=\frac{2\sqrt{a}-2+a-\sqrt{a}-a-\sqrt{a}+2\sqrt{a}+2}{\left(\sqrt{a}+1\right)\left(a-1\right)}\cdot\frac{\left(\sqrt{a}-1\right)\left(a-1\right)}{a}\)
\(=\frac{2\sqrt{a}}{\left(\sqrt{a}+1\right)\left(a-1\right)}\cdot\frac{\left(\sqrt{a}-1\right)\left(a-1\right)}{a}\)
\(=\frac{2\sqrt{a}\left(\sqrt{a-1}\right)}{a\left(\sqrt{a}+1\right)}=\frac{2\left(\sqrt{a}-1\right)}{\sqrt{a}\left(\sqrt{a}+1\right)}\)
\(N=\left(\frac{\left(\sqrt{a}+1\right)^2-\left(\sqrt{a}-1\right)^2}{a-1}+4\sqrt{a}\right)\cdot\frac{a-1}{\sqrt{a}}\)
\(=\left(\frac{a+1+2\sqrt{a}-a-1+2\sqrt{a}}{a-1}+4\sqrt{a}\right)\cdot\frac{a-1}{\sqrt{a}}\)
\(=\left(\frac{4\sqrt{a}}{a-1}+4\sqrt{a}\right)\cdot\frac{a-1}{\sqrt{a}}=4\sqrt{a}\left(\frac{1}{a-1}+1\right)\cdot\frac{a-1}{\sqrt{a}}=4\cdot\left(a-1\right)\left(\frac{1}{a-1}+1\right)\)
\(=4\cdot\left(a-1\right)\)
vừa tham khảo cách làm vừa check lại hộ tớ với nhé :33
\(Với\)\(a>0\);\(a\ne1\)ta có:
\(M=(\frac{2+\sqrt{a}}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}).(\frac{a\sqrt{a}+a-\sqrt{a}-1}{\sqrt{a}})\)
\(=[\frac{\sqrt{a}+2}{(\sqrt{a}+1)^2}-\frac{\sqrt{a}-2}{(\sqrt{a}+1)(\sqrt{a}-1)}].\frac{(a\sqrt{a}-\sqrt{a})+(\sqrt{a}-1)}{\sqrt{a}}\)
\(=[\frac{(\sqrt{a}-2).(\sqrt{a}-1)}{(\sqrt{a}+1)^2.(\sqrt{a}-1)}-\frac{(\sqrt{a}-2).(\sqrt{a}+1)}{(\sqrt{a}+1)^2.(\sqrt{a}-1)}].\frac{\sqrt{a}(a-1)+(a-1)}{\sqrt{a}}\)
\(=[\frac{a+\sqrt{a}-2}{(\sqrt{a}+1)(a-1)}-\frac{a-\sqrt{a}-2}{(\sqrt{a}+1)(a-1)}].\frac{(a-1).(\sqrt{a}+1)}{\sqrt{a}}\)
\(=\frac{a+\sqrt{a}-2-a+\sqrt{a}+2}{(a-1).(\sqrt{a}+1)}.\frac{(a-1)(\sqrt{a}+1)}{\sqrt{a}}\)
\(=\frac{2\sqrt{a}}{(a-1)(\sqrt{a}+1)}.\frac{(a-1)(\sqrt{a}+1)}{\sqrt{a}}\)
\(=2\)
Vậy \(M=2\)
\(Với\)\(a>0;a\ne1:\)\(N=(\frac{\sqrt{a}+1}{\sqrt{a}-1}-\frac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}).(\sqrt{a}-\frac{1}{\sqrt{a}})\)
\(=[\frac{(\sqrt{a}+1).(\sqrt{a}+1)}{\left(\sqrt{a}-1\right).(\sqrt{a}+1)}-\frac{(\sqrt{a}-1).(\sqrt{a}-1)}{(\sqrt{a}-1).(\sqrt{a}+1)}+\frac{4\sqrt{a}(a-1)}{(\sqrt{a}-1).(\sqrt{a}+1)}].\frac{a-1}{\sqrt{a}}\)
\(=\frac{(\sqrt{a}+1)^2-(\sqrt{a}-1)^2+(4a\sqrt{a}-4\sqrt{a})}{(\sqrt{a}-1).(\sqrt{a}+1)}.\frac{a-1}{\sqrt{a}}\)
\(=\frac{a+2\sqrt{a}+1-a+2\sqrt{a}-1+4a\sqrt{a}-4\sqrt{a}}{a-1}.\frac{a-1}{\sqrt{a}}\)
\(=\frac{4a\sqrt{a}}{a-1}.\frac{a-1}{\sqrt{a}}\)\(=4a\)
Vậy \(N=4a\)
Xem thêm câu trả lời
Rút gọn biểu thức:
A= \(\left(\frac{1}{\sqrt{a}-1}-\frac{1}{\sqrt{a}}\right):\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
\(A=\left(\frac{1}{\sqrt{a}-1}-\frac{1}{\sqrt{a}}\right):\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
\(=\frac{\sqrt{a}-\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\sqrt{a}}:\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}+2\right)\left(\sqrt{a}-2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(=\frac{1}{\left(\sqrt{a}-1\right)\sqrt{a}}:\frac{a-1-\left(a-4\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(=\frac{1}{\left(\sqrt{a}-1\right)\sqrt{a}}:\frac{3}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(=\frac{1}{\left(\sqrt{a}-1\right)\sqrt{a}}.\frac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}{3}\)
\(=\frac{\sqrt{a}-2}{3\sqrt{a}}\)
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Rút gọn biểu thức:
A= \(\left(\frac{1}{\sqrt{a}-1}-\frac{1}{\sqrt{a}}\right):\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
\(A=\left(\frac{1}{\sqrt{a}-1}-\frac{1}{\sqrt{a}}\right):\left(\frac{\sqrt{a}+1}{\sqrt{a}-2}-\frac{\sqrt{a}+2}{\sqrt{a}-1}\right).\)
\(A=\frac{\sqrt{a}-\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{a-1-a+2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(A=\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}.\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)\)
\(A=\frac{\sqrt{a}-2}{\sqrt{a}}\)
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Rút gọn A=\(\left(1-\frac{\sqrt{a}}{\sqrt{a}+1}\right):\left(\frac{\sqrt{a}+3}{\sqrt{a}-2}-\frac{\sqrt{a}+2}{\sqrt{a}-3}+\frac{\sqrt{a}+2}{x-5\sqrt{x}+6}\right)\)