rut gon ( a - \(\frac{a^2}{a+b}\))( \(\frac{1}{b}\)+ \(\frac{2}{a-b}\))
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11 tháng 10 2017
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 \(A=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}\)
11 tháng 10 2017
ĐK : tự ghi nha
\(\left(\frac{\sqrt{a}}{\sqrt{ab}-b}+\frac{2\sqrt{a}+\sqrt{b}}{\sqrt{ab}-a}\right):\left(\frac{1}{\sqrt{a}}+\frac{1}{\sqrt{b}}\right)\)
TM
1
5 tháng 8 2019
P=\(\frac{a-1}{\sqrt{b-1}}\sqrt{\frac{b-2\sqrt{b}+1}{a^2-2a+1}}=\frac{a-1}{\sqrt{b-1}}\sqrt{\frac{\left(\sqrt{b}-1\right)^2}{\left(a-1\right)^2}}=\frac{a-1}{\sqrt{b-1}}.(\frac{\sqrt{b}-1}{a-1})=\frac{\sqrt{b}-1}{\sqrt{b-1}}\)
NQ
0
24 tháng 7 2019
a) \(A=\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{6}\right)\left(\frac{1-\sqrt{a}}{1-a}\right)^2\)
\(A=\frac{\left(-\sqrt{a}+1\right)^2}{\left(-a+1\right)^2}.\left(\sqrt{a}+\frac{-a\sqrt{a}+1}{-\sqrt{a}+1}\right)\)
\(A=\frac{\left(1-\sqrt{a}\right)^2\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)}{\left(1-a\right)^2}\)
\(A=\frac{\frac{-a\sqrt{a}+\sqrt{a}.\left(-\sqrt{a}+1\right)+1}{-\sqrt{a}+1}.\left(-\sqrt{a}+1\right)^2}{\left(1-a\right)^2}\)
\(A=\frac{a^2-2a+1}{\left(1-a\right)^2}\)
\(A=\frac{\left(a-1\right)^2}{\left(1-a\right)^2}\)
\(A=1\)
HG
2
5 tháng 10 2017
A=\(\frac{a\sqrt{a}+b\sqrt{b}-\left(a+b\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}\)=\(\frac{-a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}\)=\(\frac{-\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}\left(\sqrt{a}+\sqrt{b}\right)}\)=\(-1\)
Lời giải:
$(a-\frac{a^2}{a+b})(\frac{1}{b}+\frac{2}{a-b})$
$=\frac{a(a+b)-a^2}{a+b}.\frac{a-b+2b}{b(a-b)}$
$=\frac{ab}{a+b}.\frac{a+b}{b(a-b)}=\frac{a}{a-b}$