1.Tìm x để biểu thức sau có nghĩa
a) \(A=\sqrt{\frac{2x+3}{x-3}}\)
b) \(B=\frac{\sqrt{2x+3}}{\sqrt{x-3}}\)
c)\(C=\sqrt{-\frac{5}{x+2}}\)
d) \(D=\sqrt{-x}+\frac{1}{x+3}\)
2. Rút gọn biểu thức
a) \(A=\sqrt{\frac{a+\sqrt{a^2-1}}{2}}+\sqrt{\frac{a-\sqrt{a^2-1}}{2}};\left(a>1\right)\)
b) \(B=\sqrt{\frac{a+\sqrt{a^2-b}}{2}}-\sqrt{\frac{a-\sqrt{a^2-b}}{2}}\)( \(a\) > \(\sqrt{b}\); b > \(0\))
c)\(C=\left(1+\frac{a+\sqrt{a}}{\sqrt{a+1}}\right)\left(1-\frac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)( a > 0 ; a\(\ne\)1 )
d) \(D=\frac{x^2+\sqrt{x}}{x-\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}};\left(x>0\right)\)
