i.
\(=\sqrt{\dfrac{\left(x-2\right)\left(x-2\right)}{x-2}}=\sqrt{\dfrac{x-2}{x-2}}=\sqrt{1}=1\)
j.
\(=1-\sqrt{\dfrac{\left(x-3\right)\left(x-3\right)}{x-3}}=1-\sqrt{\dfrac{x-3}{x-3}}=1-\sqrt{1}=1-1=0\)
k.
\(=1+\dfrac{x-1}{\sqrt{\left(x-1\right)^2}}=1+\dfrac{x-1}{x-1}=1+1=2\)
I.
\(=x-3-\dfrac{\sqrt{\left(x-3\right)^2}}{x-3}=x-3-\dfrac{x-3}{x-3}=x-3-1=x-4\)
i) \(\dfrac{\sqrt{\left(x-2\right)^2}}{x-2}=\dfrac{\left|x-2\right|}{x-2}=\dfrac{x-2}{x-2}=1\)
j) \(1-\dfrac{\sqrt{x^2-6x+9}}{x-3}\\ =1-\dfrac{\sqrt{\left(x-3\right)^2}}{x-3}\\ =1-\dfrac{\left|x-3\right|}{x-3}\\ =1-\left(-1\right)=2\)
k) \(1-\dfrac{1-x}{\sqrt{x^2-2x+1}}\\ =1-\dfrac{1-x}{\sqrt{\left(x-1\right)^1}}\\ =1-\dfrac{1-x}{\left|x-1\right|}\\ =1-1=0\)
l) \(\sqrt{\left(x-3\right)^2}-\dfrac{\sqrt{x^2-6x+9}}{x-3}\\ =\left|x-3\right|-\dfrac{\left|x-3\right|}{x-3}\\ =x-3-1=x-4\)
m) \(x-y-\sqrt{x^2-2xy+y^2}=x-y-\sqrt{\left(x-y\right)^2}\\ =x-y-\left|x-y\right|=x-y-x-y=-2y\)
