Question

Bài 1 Rút gọn các biểu thức sau:\

a) \(2x-1-\dfrac{\sqrt{x^2-10x+25}}{x-5}\)

b) \(\dfrac{\sqrt{x^2-4x+4}}{x^2-2}\)

c)\(\sqrt{\left(x-4\right)^2}+\dfrac{x-4}{\sqrt{x^2-8x+16}}\)

Answer 1

\(2x-1-\dfrac{\sqrt{x^2-10x+25}}{x-5}=2x-1-\dfrac{\sqrt{\left(x-5\right)^2}}{x-5}=2x-1-\dfrac{\left|x-5\right|}{x-5}=\left[{}\begin{matrix}2x-1-1=2x-2khix-5>0\\2x-1+1=2xkhix-5< 0\end{matrix}\right.\)

Answer 2

b) \(\dfrac{\sqrt{x^2-4x+4}}{x^2-2}=\dfrac{\sqrt{\left(x-2\right)^2}}{x^2-2}=\left[{}\begin{matrix}\dfrac{x-2}{x^2-2}khix-2\ge0\\\dfrac{2-x}{x^2-2}khix-2\le0\end{matrix}\right.\)

Answer 3

c) \(\sqrt{\left(x-4\right)^2}+\dfrac{x-4}{\sqrt{x^2-8x+16}}=\left|x-4\right|+\dfrac{x-4}{\sqrt{\left(x-4\right)^2}}=\left|x-4\right|+\dfrac{x-4}{\left|x-4\right|}=\left[{}\begin{matrix}x-4+1=x-3khix-4>0\\4-x-1=3-xkhix-4< 0\end{matrix}\right.\)