A=\(\left(\frac{2a+\sqrt{a}}{2\sqrt{a}+1}-5\right).\left(\frac{2a-\sqrt{a}}{2\sqrt{a}-1}+5\right)=a-25\)
Rút gọn A
Những câu hỏi liên quan
Rút gọn \(1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right)\left(\frac{a-\sqrt{a}}{2\sqrt{a}-1}\right)\)
cho biểu thức Pleft(frac{1}{1-sqrt{a}}-frac{1}{sqrt{a}}right):left(frac{2a+sqrt{a}-1}{1-a}+frac{2asqrt{a}+a-sqrt{a}}{1+asqrt{a}}right)a. rút gọn P KQfrac{1-sqrt{a}+a}{sqrt{a}}b. tính P khi afrac{sqrt{3+sqrt{5}}left(sqrt{6}+sqrt{2}right)left(sqrt{10}+sqrt{2}right)left(3-sqrt{5}right)}{2sqrt{3+sqrt{5-sqrt{13-sqrt{48}}}}}+1 KQ 7/3c. tìm x để Px lm hooj t câu c vs câu a,b, t lm hết r
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cho biểu thức \(P=\left(\frac{1}{1-\sqrt{a}}-\frac{1}{\sqrt{a}}\right):\left(\frac{2a+\sqrt{a}-1}{1-a}+\frac{2a\sqrt{a}+a-\sqrt{a}}{1+a\sqrt{a}}\right)\)
a. rút gọn P KQ=\(\frac{1-\sqrt{a}+a}{\sqrt{a}}\)
b. tính P khi \(a=\frac{\sqrt{3+\sqrt{5}}\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{10}+\sqrt{2}\right)\left(3-\sqrt{5}\right)}{2\sqrt{3+\sqrt{5-\sqrt{13-\sqrt{48}}}}}+1\) KQ =7/3
c. tìm x để P>x
lm hooj t câu c vs câu a,b, t lm hết r
10 tháng 8 2015 lúc 8:37
Rút gọn biểu thức:
\(1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right)\left(\frac{a-\sqrt{a}}{2\sqrt{a}-1}\right)\)
Điều kiện: x \(\ne\) 1; 1/4 ; x \(\ge\) 0
\(A=1+\left(\frac{\left(2a+\sqrt{a}-1\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}-\frac{\left(2a+\sqrt{a}-1\right).\sqrt{a}}{\left(1-\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}\right)\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\right)\)
\(A=1+\left(\frac{\left(2a+\sqrt{a}-1\right)\left(a+\sqrt{a}+1\right)-\left(2a+\sqrt{a}-1\right)\left(1+\sqrt{a}\right).\sqrt{a}}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}\right)\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\right)\)
\(A=1+\left(\frac{\left(2a+\sqrt{a}-1\right)\left(a+\sqrt{a}+1-a-\sqrt{a}\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}\right)\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\right)\)
\(A=1+\left(\frac{\left(2a+\sqrt{a}-1\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}\right)\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\right)\)
\(A=1+\left(\frac{\left(2\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}\right)\left(\frac{-\sqrt{a}\left(1-\sqrt{a}\right)}{2\sqrt{a}-1}\right)=1+\frac{-\sqrt{a}}{a+\sqrt{a}+1}=\frac{a+1}{a+\sqrt{a}+1}\)
Các bài tập dạng này hoàn toàn làm tương tự!!!
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Rút gọn:
A= \(1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right).\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)
Rút gọn biểu thức:
a) \(\left(\frac{\sqrt{a}+1}{\sqrt{ab}+1}+\frac{\sqrt{ab}+\sqrt{a}}{\sqrt{ab}-1}\right)\div\left(\frac{\sqrt{a}+1}{\sqrt{ab}+1}+\frac{\sqrt{ab+\sqrt{a}}}{\sqrt{ab}-1}+1\right)\)
b) \(1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right)\left(\frac{a-\sqrt{a}}{2\sqrt{a}-1}\right)\)
Rút gọn biểu thức:
A= \(1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right).\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)
\(A=1+"\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}"\times\frac{a-\sqrt{a}}{2\sqrt{a}-1}=\)
\(A="\frac{1a+\sqrt{a}-1}{1-a}-\frac{1a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}"\times\frac{a-\sqrt{a}}{1\sqrt{a}-1}\)
P/s: Ko chắc đâu nhé
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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
cho M=\(\frac{2\sqrt{a}\left(\sqrt{a}+\sqrt{2a}-\sqrt{3b}\right)+\sqrt{3b}\left(2\sqrt{a}-\sqrt{3b}\right)-2a\sqrt{a}}{a\sqrt{2}+\sqrt{3ab}}\)
rút gọn M
\(\left(\frac{3\sqrt{a}}{a+\sqrt{a}+b}-\frac{3a}{a\sqrt{a}-b\sqrt{b}}+\frac{1}{\sqrt{a}-\sqrt{b}}\right):\frac{\left(a-1\right)\left(\sqrt{a}-\sqrt{b}\right)}{\left(2a+2\sqrt{ab}+2b\right)}
\)
a. Rút gọn P
b. Tìm giá trị nguyên của a để giá trị P nguyên
a) P = \(\left(\frac{3\sqrt{a}}{a+\sqrt{a}+b}-\frac{3a}{a\sqrt{a}-b\sqrt{b}}+\frac{1}{\sqrt{a}-\sqrt{b}}\right):\frac{\left(a-1\right).\left(\sqrt{a}-\sqrt{b}\right)}{\left(2.a+2.\sqrt{ab}+2.b\right)}\)
= \(\left(\frac{3\sqrt{a}.\left(\sqrt{a}-\sqrt{b}\right)-3.a+a+\sqrt{ab}+b}{\left(\sqrt{a}-\sqrt{b}\right).\left(a+\sqrt{ab}+b\right)}\right).\frac{2.\left(a+\sqrt{ab}+b\right)}{\left(a-1\right).\left(\sqrt{a}-\sqrt{b}\right)}\)
= \(\frac{a-2.\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}.\frac{2}{\left(a-1\right).\left(\sqrt{a}-\sqrt{b}\right)}\)
= \(\frac{2}{a-1}\)
b) P nguyên <=> \(\frac{2}{a-1}\)nguyên => 2 \(⋮\)a - 1
=> ( a- 1 ) = { \(\pm\)1 ; \(\pm\) 2} => a = { -1 ; 0 ; 2 ;3 }