\(\frac{\sqrt{a}-2a}{2\sqrt{a}-1}=?\)
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\(A=1+"\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}"\times\frac{a-\sqrt{a}}{2\sqrt{a}-1}=\)
\(A="\frac{1a+\sqrt{a}-1}{1-a}-\frac{1a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}"\times\frac{a-\sqrt{a}}{1\sqrt{a}-1}\)
P/s: Ko chắc đâu nhé
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ĐKXĐ:...
\(A=1+\left(\frac{1}{1-a}-\frac{\sqrt{a}}{1-a\sqrt{a}}\right).\left(2a+\sqrt{a}-1\right)\left(\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{2\sqrt{a}-1}\right)\)
\(=1+\left(\frac{\sqrt{a}-1}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}-\frac{\sqrt{a}\left(\sqrt{a}-1\right)}{\left(1-\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}\right)\left(2\sqrt{a}-1\right)\left(\sqrt{a}+1\right).\frac{\sqrt{a}}{2\sqrt{a}-1}\)
\(=1+\left(\frac{-1}{\sqrt{a}+1}+\frac{\sqrt{a}}{a+\sqrt{a}+1}\right).\sqrt{a}\left(\sqrt{a}+1\right)\)
\(=1+\left(-1+\frac{\sqrt{a}\left(\sqrt{a}+1\right)}{a+\sqrt{a}+1}\right).\sqrt{a}\)
\(=1+\left(\frac{-a-\sqrt{a}-1+a+\sqrt{a}}{a+\sqrt{a}+1}\right).\sqrt{a}\)
\(=1-\frac{\sqrt{a}}{a+\sqrt{a}+1}=\frac{a+\sqrt{a}+1-\sqrt{a}}{a+\sqrt{a}+1}=\frac{a+1}{a+\sqrt{a}+1}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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!!!
\(\frac{\sqrt{a}-2a}{2\sqrt{a}-1}=\frac{\sqrt{a}\left(1-2\sqrt{a}\right)}{2\sqrt{a}-1}=-\sqrt{a}\)