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a) \(A=\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{6}\right)\left(\frac{1-\sqrt{a}}{1-a}\right)^2\)
\(A=\frac{\left(-\sqrt{a}+1\right)^2}{\left(-a+1\right)^2}.\left(\sqrt{a}+\frac{-a\sqrt{a}+1}{-\sqrt{a}+1}\right)\)
\(A=\frac{\left(1-\sqrt{a}\right)^2\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)}{\left(1-a\right)^2}\)
\(A=\frac{\frac{-a\sqrt{a}+\sqrt{a}.\left(-\sqrt{a}+1\right)+1}{-\sqrt{a}+1}.\left(-\sqrt{a}+1\right)^2}{\left(1-a\right)^2}\)
\(A=\frac{a^2-2a+1}{\left(1-a\right)^2}\)
\(A=\frac{\left(a-1\right)^2}{\left(1-a\right)^2}\)
\(A=1\)
Đây là đề chứng minh hả !
Phần a , b đúng r
Nhưng phần b chỗ \(\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)=\left(\sqrt{a}\right)^2-\left(\sqrt{b}\right)^2\) = a - b
Dùng hằng đẳng thức thức 3 như vậy sẽ hay hơn !
Chúc bạn học tốt!
\(P=\left(\frac{3\sqrt{a}}{a+\sqrt{ab}+b}-\frac{3a}{a\sqrt{a}-b\sqrt{b}}+\frac{1}{\sqrt{a}-\sqrt{b}}\right):\frac{\left(a-1\right)\left(\sqrt{a}-\sqrt{b}\right)}{2a+2\sqrt{ab}+2b}\)
\(=\left(\frac{3\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}{\left(a+\sqrt{ab}+b\right)\left(\sqrt{a}-\sqrt{b}\right)}-\frac{3a}{\left(a+\sqrt{ab}+b\right)\left(\sqrt{a}-\sqrt{b}\right)}+\frac{\left(a+\sqrt{ab}+b\right)}{\left(a+\sqrt{ab}+b\right)\left(\sqrt{a}-\sqrt{b}\right)}\right).\frac{2\left(a+\sqrt{ab}+b\right)}{\cdot\left(a-1\right)\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\frac{3a-3\sqrt{ab}-3a+a+\sqrt{ab}+b}{\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)}.\frac{2\left(a+\sqrt{ab}+b\right)}{\left(a-1\right)\left(\sqrt{a}-\sqrt{b}\right)}\)
\(=\frac{2\left(a-2\sqrt{ab}+b\right)\left(a+\sqrt{ab}+b\right)}{\left(\sqrt{a}-\sqrt{b}\right)^2\left(a-1\right)\left(a+\sqrt{ab}+b\right)}\)
\(=\frac{2}{a-1}\)
ĐK \(\hept{\begin{cases}a\ge0\\a\ne1\end{cases}}\)
Ta có \(P=\frac{\sqrt{a}\left(1-a\right)^2}{1+a}:\left[\left(\frac{\left(1-\sqrt{a}\right)\left(a+\sqrt{a}+1\right)}{1-\sqrt{a}}+\sqrt{a}\right).\left(\frac{\left(1+\sqrt{a}\right)\left(a-\sqrt{a}+1\right)}{1+\sqrt{a}}-\sqrt{a}\right)\right]\)
\(=\frac{\sqrt{a}\left(1-a\right)^2}{1+a}:\left[\left(a+2\sqrt{a}+1\right).\left(a-2\sqrt{a}+1\right)\right]\)
\(=\frac{\sqrt{a}\left(1-a\right)^2}{1+a}.\frac{1}{\left(\sqrt{a}+1\right)^2\left(\sqrt{a}-1\right)^2}=\frac{\sqrt{a}}{1+a}\)
tham khao nha
\(A=\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)
\(A=\left(\frac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{a}\left(\sqrt{b}-\sqrt{a}\right)}\right):\left(\frac{\sqrt{b}+\sqrt{a}}{\sqrt{ab}}\right)\)
\(A=\left(\frac{\sqrt{a}}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}-\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}\right).\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)
\(A=\frac{a-2\sqrt{ab}+b}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}.\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)
\(A=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}.\frac{\sqrt{ab}}{\sqrt{b}+\sqrt{a}}\)
\(A=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
vay \(A=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
ĐK : tự ghi nha
\(\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)