= \(\sqrt{x-4+4\sqrt{x-4}+4}+\sqrt{x-4-4\sqrt{x-4}+4}-2\)
=\(\sqrt{\left(\sqrt{x-4}+2\right)^2}+\sqrt{\left(\sqrt{x-4}-2\right)^2}+2\)
=\(\sqrt{x-4}+2+\sqrt{x-4}-2+2\)
=\(2\sqrt{x-4}+2\)
Rút gọn : a) \(\dfrac{a\sqrt{b}-b\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\sqrt{ab}\)
b)\(\dfrac{x+4y-4\sqrt{xy}}{\sqrt{x}-2\sqrt{y}}+\dfrac{y+\sqrt{xy}}{\sqrt{x}+\sqrt{y}}\left(x\ge0;y\ge0;x\ne4y\right)\)
c)\(\dfrac{x+4\sqrt{x}+4}{\sqrt{x}+2}+\dfrac{4-x}{\sqrt{x}-2}\left(x\ge0;x\ne4\right)\)
d)\(\dfrac{9-x}{\sqrt{3x}+3}-\dfrac{9-6\sqrt{x}+x}{\sqrt{x}-3}\)
e)\(\dfrac{\left(\sqrt{x}-\sqrt{y}\right)^2+4\sqrt{xy}}{\sqrt{x}+\sqrt{y}}-\dfrac{x\sqrt{y}+y\sqrt{x}}{\sqrt{xy}}\)
g)\(\left(2-\dfrac{a-3\sqrt{a}}{\sqrt{a}-3}\right)\left(2-\dfrac{5\sqrt{a}-\sqrt{ab}}{\sqrt{b}-5}\right)với\) a, b \(\ge\)0 , a \(\ne\)9; b\(\ne\)25
Mọi người giúp tớ với , cảm ơn nhiều nhiều ạ !!
Rút gọn biểu thức:
\(A=\frac{10\sqrt{x}}{x+3\sqrt{x}-4}-\frac{2\sqrt{x}-3}{\sqrt{x}+4}+\frac{\sqrt{x}+1}{1-\sqrt{x}}\) \(\left(x\ge0;x\ne1\right)\)
\(\left(\dfrac{4\sqrt{x}}{2+\sqrt{x}}+\dfrac{8}{4-x}\right):\left(\dfrac{\sqrt{x}-1}{x-2\sqrt{x}}-\dfrac{2}{\sqrt{x}}\right)\)
Cho \(x,y\ge0\) thỏa mãn \(x+y=2\sqrt{3}.\)Tìm Max:
\(P=\left(x^4+1\right)\left(y^4+1\right)\)
A=\(\left(\frac{\sqrt{x}-1}{x-4}-\frac{\sqrt{x+1}}{x+4\sqrt{x+4}}\right)\):\(\frac{x\sqrt{x}}{\left(4-x\right)^2}\)
B=\(\left(\frac{2\sqrt{x}}{\sqrt{x}-3}-\frac{x+9\sqrt{x}}{x-9}\right):\frac{x\sqrt{x}}{\left(4-x\right)^2}\)
rút gọn các biểu thức
Rút gọn biểu thức :
a) \(A=\frac{x}{x-4}+\frac{1}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\) đkxđ : \(x\ge0;x\ne4\)
b) \(B=\left(\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{\sqrt{x}+1}{\sqrt{x}-1}\right)\left(\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}\right)^2\)
c) \(C=\left(\frac{1}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x+1}}\right)\div\frac{\sqrt{x}}{x+\sqrt{x}}\) đkxđ : x > 0
Cho A=\(\frac{\sqrt{x}}{\sqrt{x}+1}+\frac{3}{\sqrt{x}+1}-\frac{6\sqrt{x}-4}{x-1}\left(x\ge0;x\ne1\right)\)
Tìm GTNN của A
\(\dfrac{\sqrt{x-\sqrt{4\left(x-1\right)}}+\sqrt{x+\sqrt{4\left(x-1\right)}}}{\sqrt{x^2-4\left(x-1\right)}}\left(1-\dfrac{1}{x-1}\right)\) (với \(x>1;x\ne2\))
rút gọn biểu thức sau
D=\(\left(\sqrt{x-\sqrt{18}}-\sqrt{x+\sqrt{18}}\right)\sqrt{x+\sqrt{x^2-18}}\) với \(x\ge18\)
A=\(\sqrt{x+6\sqrt{x-9}}+\sqrt{x-6\sqrt{x-9}}\)
C=\(\dfrac{\sqrt{2-\sqrt{2-4-x^2}}\left[\sqrt{\left(2+x\right)^3}+\sqrt{\left(2-x\right)^3}\right]}{4-\sqrt{4-x^2}}\)
