\(A=\cos15^o+\dfrac{2\sin50^o}{2\cos40^o}+\sin75^o.\\ A=\cos15^o+\dfrac{2\sin50^o}{2\cos\left(90^o-40^o\right)}+\cos\left(90^o-75^o\right).\\ A=\cos15^o+\dfrac{\sin50^o}{\sin50^o}+\cos15^o.\\ A=2\cos15^o+1.\)
a) \(\dfrac{a-1}{\sqrt{b}-1}\).\(\sqrt{\dfrac{b-2\sqrt{b}+1}{\left(a-1\right).4}}\) (a,b≠1,b>0)
b) (1+\(\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\)).(1-\(\dfrac{a-\sqrt{a}}{\sqrt{a-1}}\)) (a≠1,a>0)
A= \(\dfrac{2\sqrt{a}}{\sqrt{a}+3}\)+\(\dfrac{\sqrt{a}+1}{\sqrt{a}-3}\)+\(\dfrac{3+7\sqrt{a}}{9-a}\)
P=\(\frac{a\sqrt{a}-8}{a+2\sqrt{a}+4}.\frac{a+5\sqrt{a}+6}{a-4}\) (0≤a≠4)
Rút gọn: \(A=\left(1+\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\left(1-\dfrac{a+2\sqrt{a}}{2+\sqrt{a}}\right)\)
Rút gọn các biểu thức
\(A=\left(\frac{\sqrt{a}-2}{\sqrt{a}+2}-\frac{\sqrt{a}+2}{\sqrt{a}-2}\right)\left(\sqrt{a}-\frac{4}{\sqrt{a}}\right)\)
\(B=\frac{1}{1-\sqrt{a}}+\frac{a\sqrt{a}}{\sqrt{a}-1}\)
Chứng minh đẳng thức
a) căn a/căn a - căn b - căn b/căn a + căn b - 2b/a-b = 1
b) a. căn b + b/ a-b . căn (b^2 -2 .(căn a.b^2 ) +ab/a. (a-2.căn b ) +b . ( căn a + căn b) + b
\(\left(1+\dfrac{\sqrt{a}}{a+1}\right):\left(\dfrac{1}{\sqrt{a-1}}-\dfrac{2\sqrt{a}}{a\sqrt{a}+\sqrt{a}-a-1}\right)\\ a,TìmađểbiểuthứcAcónghĩa.Rútgọn\\ b,TínhgiátrịcủaAkhia=\dfrac{2}{7+3\sqrt{5}}\\ c,TìmasaochoA< 1\)
Rút gọn :\(\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1-\sqrt{a}}{1-a}\right)^2\) với a >0 ;a ≠0
Cho biểu thức: P= (\(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\))(\(\frac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\))
a, Rút gọn P
b, Tìm a để P < 7 - 4\(\sqrt{3}\)
(1+\(\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\))(1\(\dfrac{a-\sqrt{a}}{1-\sqrt{a}}\)) với a≥0 ,a≠1
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