ĐKXĐ: \(x\ge1\)
\(=\sqrt{x+3-2\sqrt{\left(x-1\right)\left(x+3\right)}+x-1}\)
\(=\sqrt{\left(\sqrt{x+3}-\sqrt{x-1}\right)^2}\)
\(=\left|\sqrt{x+3}-\sqrt{x-1}\right|\)
\(=\sqrt{x+3}-\sqrt{x-1}\)
RUT GON:
\(\sqrt{2x+1-2\sqrt{\left(x-1\right)\left(x+2\right)}}\)
Rut gon bt C=\(\dfrac{\sqrt{4x+4+\dfrac{1}{x}}}{\sqrt{x}.\left|2x^2-x-1\right|}\)
rut gon bieu thuc 2x2\(\sqrt{\frac{9}{x^4}}\) voi x<0
rut gon biểu thức ;
\(\dfrac{\sqrt[3]{4}+\sqrt[3]{2}+2}{\sqrt[3]{4}+\sqrt[3]{2}+1}\)
rut gon \(\frac{x-11}{\sqrt{x-2}-3}\)
cho P=\(\left(\dfrac{3}{\sqrt{x}-1}+\dfrac{\sqrt{x}-3}{x-1}\right):\left(\dfrac{x+2}{x+\sqrt{x}-2}-\dfrac{\sqrt{x}}{\sqrt{x}+2}\right)\\ \)
a, rut gon
b, tim x de P=\(\sqrt{x}-1\)
\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
a, rut gon A
b, tinh A voi \(4-2\sqrt{3}\)
Tìm ĐKXĐ rồi rút gon:
\(B=\dfrac{\sqrt{x^3}}{\sqrt{xy}-2y}-\dfrac{2x}{x+\sqrt{x}-2\sqrt{xy}-2\sqrt{y}}.\dfrac{1-x}{1-\sqrt{x}}\)
Mọi người giúp em với
rut gon bieu thuc:\(\sqrt{\frac{a+\sqrt{a^2-b}}{2}}+\frac{a\sqrt{a^2-b}}{2}\)