Rút gọn:
\(A=\frac{x^2+5x+6+x\sqrt{9-x^2}}{3x-x^2+\left(x+2\right).\sqrt{9-x^2}}\)
\(B=\frac{x^2-5x+6+3\sqrt{x^2-6x+8}}{3x-12+\left(x-3\right).\sqrt{x^2-6x+8}}\)
\(C=\frac{\sqrt{2\sqrt{4-x^2}}.\left(\sqrt{\left(2+x\right)^3}-\sqrt{\left(2-x\right)^3}\right)}{4+\sqrt{4-x^2}}\)
Cho \(A=\frac{8\sqrt{x}+8}{6\sqrt{x}+9}\)
Tìm x nguyên để A nguyên
\(\sqrt{12-\frac{12}{x^2} }+\sqrt{x^2+\frac{12}{x} }=x^2+\frac{25}{2} \)
\(\frac{\sqrt[3]{10-x}+\sqrt[3]{8-x}}{\sqrt[3]{10-x}-\sqrt[3]{8-x}}=9-x \)
\(4x^2+\sqrt{2x+1}+5=12x\)
* Tìm x, bt:
a.\(\sqrt{\left(2x+3\right)^2}=8\)
b.\(\sqrt{9x}-7\sqrt{x}=8-6\sqrt{x}\)
c.\(\sqrt{9x-9}+1=13\)
cho biểu thức P = (\(\frac{3\sqrt{x}}{\sqrt{x}+2}\) + \(\frac{\sqrt{x}}{2-\sqrt{x}}\) +\(\frac{8\sqrt{x}}{x-4}\) ) : ( 2 - \(\frac{2\sqrt{x}+3}{\sqrt{x}+2}\) )
a) rút gọn P
b) tính P khi x = \(\frac{8}{3+\sqrt{5}}\)
c) tìm gtnn của P khi x > 4
d) tìm x ϵ Z để P ϵ Z
1, \(\frac{x}{2}-\frac{3-x}{3}=\frac{2x+2}{5}\)
2,1-\(\frac{3-x}{3}=\frac{2x+2}{5}-\frac{2-x}{4}\)
3,\(\frac{2}{3}x+1=x-5\)
4, 2x-x2 =0
5,\(\frac{4x}{x+1}+\frac{x+3}{x}=6\)
6, \(\frac{x-1}{x-3}+\frac{2x+2}{x-2}=8\)
7, \(\sqrt{x-1}=\sqrt{2}\)
8, \(\sqrt{2x-1}=\sqrt{x}-4\)
\(\frac{x\sqrt{x}-2x+28}{x-3\sqrt{x}-4}-\frac{\sqrt{x}-4}{\sqrt{x}+1}-\frac{\sqrt{x}+8}{\sqrt{x}-4}\)
CHo biểu thức A=\(\frac{8-x}{2+\sqrt[3]{x}}:?\left(2+\frac{\sqrt[3]{x^2}}{2+\sqrt[3]{x}}\right)+\left(\sqrt[3]{x}+\frac{2\sqrt[3]{x}}{\sqrt[3]{x}-2}\right)\frac{\sqrt[3]{x^2}-4}{\sqrt[3]{x^2}+2\sqrt[3]{x}}\) vỚI x khác 8,-8,0. CMR gt A ko phụ thuộc vào x
LÀM ON GIÚP
\(Q=\left(\frac{\sqrt{x}-1}{3\sqrt{x}-1}-\frac{1}{3\sqrt{x}+x}+\frac{8\sqrt{x}}{9x-1}\right)\div\left(1-\frac{3\sqrt{x}-2}{3\sqrt{x}+1}\right)\)