\(\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1-\sqrt{a}}{1-a}\right)^2\) giai phuong trinh
Những câu hỏi liên quan
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
\(A=\left(1+\frac{\sqrt{a}-1}{a-\sqrt{a}}\right):\left(\frac{a+\sqrt{a}}{a-1}\frac{\sqrt{a}}{a-\sqrt{a}}\right)\)
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}+\frac{2}{a-1}\right)\)
\(C=\left(\frac{\sqrt{a}}{\sqrt{a}+1}-\frac{\sqrt{a}}{\sqrt{a}-1}+\frac{1}{a-1}\right):\frac{a}{2+2\sqrt{a}}\)
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}
Đọc tiếp
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) \(\frac{\sqrt{a}+\sqrt{b}-1}{a+\sqrt{ab}}+\frac{\sqrt{a}-\sqrt{b}}{2\sqrt{ab}}.\left(\frac{\sqrt{b}}{a-\sqrt{ab}}+\frac{\sqrt{b}}{a+\sqrt{ab}}\right)=\frac{\sqrt{a}}{a}\)
Qleft(frac{2}{2+2sqrt{a}}+frac{1}{2-2sqrt{a}}-frac{a^2+1}{1-a^2}right)left(1+frac{1}{a}right)left(frac{1}{2left(1+sqrt{a}right)}+frac{1}{2left(1-sqrt{a}right)}-frac{a^2+1}{left(1-sqrt{a}right)left(1+sqrt{a}right)left(1+aright)}right)left(frac{a+1}{a}right)left(frac{left(1-sqrt{a}right)left(1+aright)+left(1+sqrt{a}right)left(1+aright)-2left(a^2+1right)}{2left(1-aright)left(1+aright)}right)left(frac{a+1}{a}right)left(frac{1+a-sqrt{a}-asqrt{a}+1+a+sqrt{a}+asqrt{a}-2a^2-2}{2left(1-aright)left(1+arig...
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\(Q=\left(\frac{2}{2+2\sqrt{a}}+\frac{1}{2-2\sqrt{a}}-\frac{a^2+1}{1-a^2}\right)\left(1+\frac{1}{a}\right)\)
\(=\left(\frac{1}{2\left(1+\sqrt{a}\right)}+\frac{1}{2\left(1-\sqrt{a}\right)}-\frac{a^2+1}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(1+a\right)}\right)\left(\frac{a+1}{a}\right)\)
\(=\left(\frac{\left(1-\sqrt{a}\right)\left(1+a\right)+\left(1+\sqrt{a}\right)\left(1+a\right)-2\left(a^2+1\right)}{2\left(1-a\right)\left(1+a\right)}\right)\left(\frac{a+1}{a}\right)\)
\(=\left(\frac{1+a-\sqrt{a}-a\sqrt{a}+1+a+\sqrt{a}+a\sqrt{a}-2a^2-2}{2\left(1-a\right)\left(1+a\right)}\right)\left(\frac{a+1}{a}\right)\)
\(=\left(\frac{2a-2a^2}{2\left(1-a\right)\left(1+a\right)}\right)\)
\(=\frac{a}{a}\)= 1
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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Rút gọn biểu thức:
1) Pfrac{x^2-sqrt{x}}{x+sqrt{x}+1}-frac{2x+sqrt{x}}{sqrt{x}}+frac{2cdotleft(x-1right)}{sqrt{x}-1}
2) Pleft(frac{sqrt{x}-2}{sqrt{x}-1}-frac{sqrt{x}+2}{x+2sqrt{x}+1}right)cdotfrac{left(1-xright)^2}{2}
3) Bleft(frac{1-asqrt{a}}{1-sqrt{a}}+sqrt{a}right)cdotleft(frac{1+asqrt{a}}{1+sqrt{a}}-sqrt{a}right)
4) Kleft(frac{sqrt{a}}{sqrt{a}-1}-frac{1}{a-sqrt{a}}right)divleft(frac{1}{sqrt{a}+1}-frac{2}{a-1}right)
Đọc tiếp
Rút gọn biểu thức:
1) \(P=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\cdot\left(x-1\right)}{\sqrt{x}-1}\)
2) \(P=\left(\frac{\sqrt{x}-2}{\sqrt{x}-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\cdot\frac{\left(1-x\right)^2}{2}\)
3) \(B=\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\cdot\left(\frac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\)
4) \(K=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right)\div\left(\frac{1}{\sqrt{a}+1}-\frac{2}{a-1}\right)\)
Cho A=\(\left[1:\left(1-\frac{\sqrt{a}}{1+\sqrt{a}}\right)\right]\left[\frac{1}{\sqrt{a}-1}-\frac{2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}-1\right)}\right]\)
= \(1:\frac{1+\sqrt{a}-\sqrt{a}}{1+\sqrt{a}}.\frac{a+1-2\sqrt{a}}{\left(a+1\right)\left(\sqrt{a}-1\right)}\)
=\(1:\frac{1}{\sqrt{a}+1}.\frac{\left(\sqrt{a}-1\right)^2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)\left(\sqrt{a}-1\right)}\)
=\(\left(\sqrt{a}+1\right)\frac{1}{\sqrt{a}+1}\)
=\(1\)
\(\left(\frac{1}{\sqrt{a}+\sqrt{a+1}}+\frac{1}{\sqrt{a}-\sqrt{a-1}}\right):\left(1+\sqrt{\frac{a+1}{a-1}}\right)\)
\(\left(\frac{\left(\sqrt{a}+1\right)\left(a-\sqrt{ab}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a^3}+3\right)\left(a-b\right)}\right)\)
Rút gọn 2 biểu thức trên?
Ai giúp mình với, tks nhiều
mi tích tau tau tích mi xong tau trả lời nka
việt nam nói là làm
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V=\(\left(\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+1}\right)\left(\frac{x-1}{\sqrt{x}+1}-2\right)\)
W= \(\left(\frac{\sqrt{a}-1}{3\sqrt{a}+\left(\sqrt{a}-1\right)^2}-\frac{1-3\sqrt{a}+a}{a\sqrt{a}-1}-\frac{1}{\sqrt{a}-1}\right):\frac{a+1}{1-\sqrt{a}}\)
ĐKXĐ:...
\(V=\left(\frac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\left(\frac{x-1-2\left(\sqrt{x}+1\right)}{\sqrt{x}+1}\right)\)
\(=\left(\frac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right)\left(\frac{x-2\sqrt{x}-3}{\sqrt{x}+1}\right)=\frac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+1\right)}=\frac{2\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(W=\left(\frac{\sqrt{a}-1}{a+\sqrt{a}+1}-\frac{a-3\sqrt{a}+1}{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}-\frac{1}{\sqrt{a}-1}\right).\left(\frac{1-\sqrt{a}}{a+1}\right)\)
\(=\left(\frac{\left(\sqrt{a}-1\right)^2-a+3\sqrt{a}-1-\left(a+\sqrt{a}+1\right)}{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\right)\left(\frac{1-\sqrt{a}}{a+1}\right)\)
\(=\left(\frac{-\left(a+1\right)}{\left(\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)}\right)\left(\frac{-\left(\sqrt{a}-1\right)}{a+1}\right)=\frac{1}{a+\sqrt{a}+1}\)
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