a)\(=-\sqrt{\left(\frac{a}{b}\right)^2\cdot\frac{b}{a}}\)
\(=-\sqrt{\frac{a^2}{b^2}\cdot\frac{b}{a}}\)
\(=-\sqrt{\frac{a}{b}}\)
b) \(=\sqrt{\left(\frac{1}{2x-1}\right)^2\cdot5\left(4x^2-4x+1\right)}\)
\(=\sqrt{\frac{5}{\left(2x-1\right)^2}\cdot\left(2x-1\right)^2}\)
\(=\sqrt{5}\)
c)\(=\sqrt{\left(x-5\right)^2\cdot\frac{-3}{\left(x-5\right)\left(x+5\right)}}\)
\(=\sqrt{\frac{-3\left(x-5\right)}{x+5}}\)
\(=\sqrt{\frac{15-3x}{x+5}}\)
d)\(=\sqrt{\left(\frac{x}{x-y}\right)^2\cdot\frac{\left(x-y\right)}{x}}\)
\(=\sqrt{\frac{x^2}{\left(x-y\right)^2}\cdot\frac{x-y}{x}}\)
\(=\sqrt{\frac{x}{x-y}}\)