\(\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)\left(\frac{a-\sqrt{a}}{\sqrt{a}+1}-\frac{a+\sqrt{a}}{\sqrt{a}-1}\right)\)
giúp mk vs ạ
Những câu hỏi liên quan
\(A=\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}-\frac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}+\frac{1}{\sqrt{a}}\right)voix>0,x\ne1,kq=4a\)
đề iu cầu là rút gọn biểu thức ạ các bn giải giúp mk vs sáng mai phải nộp cô rồi ạ
\(A=\left(\frac{\left(\sqrt{a}+1\right)^2-\left(\sqrt{a}-1\right)^2}{a-1}+4\sqrt{a}\right)\left(\frac{a+1}{\sqrt{a}}\right)\)
\(A=\left(\frac{4\sqrt{a}}{a-1}+\frac{4\sqrt{a}\left(a-1\right)}{a-1}\right)\left(\frac{a+1}{\sqrt{a}}\right)\)
\(A=\frac{4a\sqrt{a}}{a-1}.\frac{a+1}{\sqrt{a}}=\frac{4a\left(a+1\right)}{a-1}\)
....... Tới đây được chưa bạn?
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C/m biểu thứca)left(frac{asqrt{a}+bsqrt{b}}{sqrt{a}+sqrt{b}}-sqrt{ab}right)left(frac{sqrt{a}+sqrt{b}}{a-b}right)1(a,b0,ane0b)frac{a-b-2sqrt{ab}}{sqrt{a}-sqrt{b}}:frac{1}{sqrt{a}+sqrt{b}}a-bleft(a,b0,ane bright)c)left(2+frac{a-sqrt{a}}{sqrt{a}-1}right)left(2-frac{a+sqrt{a}}{sqrt{a}+1}right)4-aleft(a0,ane1right)d)left(frac{1-asqrt{a}}{1-sqrt{a}}+sqrt{a}right)left(frac{1+asqrt{a}}{1+sqrt{a}}-sqrt{a}right)left(1-aright)^2left(age0,ane1right)Giải giúp mk với. THứ 3 tuần sau là phải nộp rồi
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C/m biểu thức
a)\(\left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\left(\frac{\sqrt{a}+\sqrt{b}}{a-b}\right)=1\)(a,b>0,a\(\ne\)0
b)\(\frac{a-b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}:\frac{1}{\sqrt{a}+\sqrt{b}}=a-b\left(a,b>0,a\ne b\right)\)
c)\(\left(2+\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(2-\frac{a+\sqrt{a}}{\sqrt{a}+1}\right)=4-a\left(a>0,a\ne1\right)\)
d)\(\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)=\left(1-a\right)^2\left(a\ge0,a\ne1\right)\)
Giải giúp mk với. THứ 3 tuần sau là phải nộp rồi
\(\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\)
giải vs ạ
\(\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\) (\(a>0;a\ne1\))
=\(\left(\frac{a}{\sqrt{a}\left(\sqrt{a}-1\right)}-\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right)\):\(\left(\frac{\sqrt{a}-1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}+\frac{2}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right)\)
=\(\frac{a-1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{\sqrt{a}+1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\)
=\(\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}.\left(\sqrt{a}-1\right)\)
\(=\frac{a-1}{\sqrt{a}}\)
vậy...
Rút gọn rồi tính giá trị của biểu thứcsqrt{frac{sqrt{a}-1}{sqrt{b}+1}}divsqrt{frac{sqrt{b}-1}{sqrt{a}+1}}vớia7,25;b3,25 frac{a-b}{sqrt{atimesleft(a+2times bright)+b^2}}divsqrt{frac{left(a-bright)^2}{atimesleft(a+bright)}}vớiab0vàfrac{a}{b}frac{9}{7} frac{x-1}{sqrt{y}-1}timessqrt{frac{left(y-2timessqrt{y}+1right)^2}{left(x-1right)^4}}vớixfrac{-1}{2};y121; giúp mk vs
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Rút gọn rồi tính giá trị của biểu thức
\(\sqrt{\frac{\sqrt{a}-1}{\sqrt{b}+1}}\div\sqrt{\frac{\sqrt{b}-1}{\sqrt{a}+1}}vớia=7,25;b=3,25\)
\(\frac{a-b}{\sqrt{a\times\left(a+2\times b\right)+b^2}}\div\sqrt{\frac{\left(a-b\right)^2}{a\times\left(a+b\right)}}vớia>b>0và\frac{a}{b}=\frac{9}{7}\)
\(\frac{x-1}{\sqrt{y}-1}\times\sqrt{\frac{\left(y-2\times\sqrt{y}+1\right)^2}{\left(x-1\right)^4}}vớix=\frac{-1}{2};y=121\); giúp mk vs
Giúp mình nhé, mình đang càn gấp :a) left(1+frac{a-sqrt{a}}{sqrt{a}-1}right)left(1-frac{a+sqrt{a}}{1+sqrt{a}}right)b) left(2-frac{a-3sqrt{a}}{sqrt{a}-3}right)left(2-frac{5sqrt{a}-sqrt{ab}}{sqrt{b}-5}right)c) left(3+frac{a-2sqrt{a}}{sqrt{a}-2}right)left(3-frac{3a+sqrt{a}}{3sqrt{a}+1}right)d) left(frac{a-sqrt{a}}{sqrt{a}-1}+2right)left(2-frac{sqrt{a}+a}{1+sqrt{a}}right)
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Giúp mình nhé, mình đang càn gấp :<<<
a) \(\left(1+\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(1-\frac{a+\sqrt{a}}{1+\sqrt{a}}\right)\)
b) \(\left(2-\frac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\frac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)\)
c) \(\left(3+\frac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(3-\frac{3a+\sqrt{a}}{3\sqrt{a}+1}\right)\)
d) \(\left(\frac{a-\sqrt{a}}{\sqrt{a}-1}+2\right)\left(2-\frac{\sqrt{a}+a}{1+\sqrt{a}}\right)\)
\(a,\left(1+\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(1-\frac{a+\sqrt{a}}{1+\sqrt{a}}\right)=\left(1+\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right)\left(1-\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\)
\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)=1^2-\sqrt{a}^2=1-a\)
\(b,\left(2-\frac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\frac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)=\left(2-\frac{\sqrt{a}\left(\sqrt{a}-3\right)}{\sqrt{a}-3}\right)\left(2-\frac{-\sqrt{a}\left(\sqrt{b}-5\right)}{\sqrt{b}-5}\right)\)
\(=\left(2-\sqrt{a}\right)\left(2+\sqrt{a}\right)=2^2-\sqrt{a}^2=2-a\)
\(c,\left(3+\frac{a-2\sqrt{a}}{\sqrt{a}-2}\right)\left(3-\frac{3a+\sqrt{a}}{3\sqrt{a}+1}\right)=\left(3+\frac{\sqrt{a}\left(\sqrt{a}-2\right)}{\sqrt{a}-2}\right)\left(3-\frac{\sqrt{a}\left(3\sqrt{a}+1\right)}{3\sqrt{a}+1}\right)\)
\(=\left(3+\sqrt{a}\right)\left(3-\sqrt{a}\right)=3^2-\sqrt{a}^2=3-a\)
\(d,\left(\frac{a-\sqrt{a}}{\sqrt{a}-1}+2\right)\left(2-\frac{\sqrt{a}+a}{1+\sqrt{a}}\right)=\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}+2\right)\left(2-\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right)\)
\(=\left(\sqrt{a}+2\right)\left(2-\sqrt{a}\right)=2^2-\sqrt{a}^2=2-a\)
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\(A=\left(\frac{4\sqrt{y}\left(2-\sqrt{y}\right)+8y}{\left(2+\sqrt{y}\right)\left(2-\sqrt{y}\right)}\right):\left(\frac{\sqrt{y}-1}{y-2\sqrt{y}}-\frac{2}{\sqrt{y}}\right)\)
a) rút gọn
b) tìm y để A = -2
giúp mk vs ạ, mik c.ơn
ĐKXĐ: \(y\ge0;y\ne4;9\)
\(A=\left(\frac{8\sqrt{y}-4y+8y}{\left(2+\sqrt{y}\right)\left(2-\sqrt{y}\right)}\right):\left(\frac{\sqrt{y}-1}{\sqrt{y}\left(\sqrt{y}-2\right)}-\frac{2\left(\sqrt{y}-2\right)}{\sqrt{y}\left(\sqrt{y}-2\right)}\right)\)
\(=\left(\frac{4\sqrt{y}\left(2+\sqrt{y}\right)}{\left(2+\sqrt{y}\right)\left(2-\sqrt{y}\right)}\right):\left(\frac{-\sqrt{y}+3}{\sqrt{y}\left(\sqrt{y}-2\right)}\right)\)
\(=\left(\frac{4\sqrt{y}}{2-\sqrt{y}}\right):\left(\frac{\sqrt{y}-3}{\sqrt{y}\left(2-\sqrt{y}\right)}\right)\)
\(=\frac{4\sqrt{y}}{\left(2-\sqrt{y}\right)}.\frac{\sqrt{y}\left(2-\sqrt{y}\right)}{\left(\sqrt{y}-3\right)}=\frac{4y}{\sqrt{y}-3}\)
\(A=-2\Leftrightarrow\frac{4y}{\sqrt{y}-3}=-2\)
\(\Rightarrow2y=-\sqrt{y}+3\Rightarrow2y+\sqrt{y}-3=0\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{y}=1\\\sqrt{y}=-\frac{3}{2}< 0\left(l\right)\end{matrix}\right.\) \(\Rightarrow y=1\)
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Chứng minh các đẳng thức sau: a) left(1-a^2right):left[left(frac{1-asqrt{a}}{1-sqrt{a}}+sqrt{a}right)left(frac{1
+asqrt{a}}{1+sqrt{a}}-sqrt{a}right)right]+1frac{2}{1-a}b) left(sqrt{a}+frac{b-sqrt{ab}}{sqrt{a}+sqrt{b}}right):left(frac{a}{sqrt{ab}+b}
+frac{b}{sqrt{ab}-a}-frac{a+b}{sqrt{ab}}right)sqrt{b}-sqrt{a}c) frac{sqrt{a}+sqrt{b}-1}{a
+sqrt{ab}}+frac{sqrt{a}-sqrt{b}}{2sqrt{ab}}left(frac{sqrt{b}}{a-sqrt{ab}}+frac{sqrt{b}}{a
+sqrt{ab}}right)frac{sqrt{a}}{a}d) left(frac{asqrt{a}+bsqrt{b}}{sqrt{a}...
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Chứng minh các đẳng thức sau:
a) \(\left(1-a^2\right):\left[\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1
+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\right]+1=\frac{2}{1-a}\)
b) \(\left(\sqrt{a}+\frac{b-\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\right):\left(\frac{a}{\sqrt{ab}+b}
+\frac{b}{\sqrt{ab}-a}-\frac{a+b}{\sqrt{ab}}\right)=\sqrt{b}-\sqrt{a}\)
c) \(\frac{\sqrt{a}+\sqrt{b}-1}{a
+\sqrt{ab}}+\frac{\sqrt{a}-\sqrt{b}}{2\sqrt{ab}}\left(\frac{\sqrt{b}}{a-\sqrt{ab}}+\frac{\sqrt{b}}{a
+\sqrt{ab}}\right)=\frac{\sqrt{a}}{a}\)
d) \(\left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right)\left(\frac{\sqrt{a}+\sqrt{b}}{a-b}\right)^2=1\)
Rút gọn các biểu thức
\(A=\left(1+\frac{\sqrt{a}-1}{a-\sqrt{a}}\right):\left(\frac{a+\sqrt{a}}{a-1}\frac{\sqrt{a}}{a-\sqrt{a}}\right)\)
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\)
\(C=\left(\frac{\sqrt{a}}{\sqrt{a}+1}-\frac{\sqrt{a}}{\sqrt{a}-1}+\frac{1}{a-1}\right):\frac{a}{2+2\sqrt{a}}\)
Bai 1)Aleft(frac{sqrt{a}}{2}-frac{1}{2sqrt{a}}right)^2left(frac{sqrt{a}-1}{sqrt{a}+1}-frac{sqrt{a}+1}{sqrt{a}-1}right),a)rút gọn A 2) B1+left(frac{2a+sqrt{a}-1}{1-a}-frac{2asqrt{a}-sqrt{a}-1}{1-asqrt{a}}right).left(frac{a-sqrt{a}}{2sqrt{a}-1}right),a) rút gọn B b) tìm a để Bfrac{sqrt{6}}{1+sqrt{6}}c) chứng minh rằng B2/3 Giúp mk với nếu đúng mk tick cho nha ,cảm ơn
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Bai 1)A=\(\left(\frac{\sqrt{a}}{2}-\frac{1}{2\sqrt{a}}\right)^2\left(\frac{\sqrt{a}-1}{\sqrt{a}+1}-\frac{\sqrt{a}+1}{\sqrt{a}-1}\right),\)
a)rút gọn A
2) B=1+\(\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}-1}{1-a\sqrt{a}}\right).\left(\frac{a-\sqrt{a}}{2\sqrt{a}-1}\right),\)
a) rút gọn B
b) tìm a để B=\(\frac{\sqrt{6}}{1+\sqrt{6}}\)
c) chứng minh rằng B>2/3
Giúp mk với nếu đúng mk tick cho nha ,cảm ơn
