Question

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

Answer 1

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

\(=\sqrt{\left(x-4\right)^2}+\dfrac{x-4}{\sqrt{\left(x-4\right)^2}}\)

\(=\left|x-4\right|+\dfrac{x-4}{\left|x-4\right|}\)

`@` Với \(x\ge4\) \(\Rightarrow x-4+\dfrac{x-4}{x-4}=x-4+1=x-3\)

`@` Với \(x< 4\) \(\Rightarrow4-x+\dfrac{x-4}{4-x}=4-x-\dfrac{4-x}{4-x}=4-x-1=3-x\)