Question

Rút gọn biểu thức sau

|x-2| + căn x^2-4x+4/x-2

Answer 1

ĐKXĐ: \(x\ne2\)

Ta có:

\(\left|x-2\right|+\frac{\sqrt{x^2-4x+4}}{x-2}=\left|x-2\right|+\frac{\sqrt{\left(x-2\right)^2}}{x-2}=\left|x-2\right|+\frac{\left|x-2\right|}{x-2}\left(1\right)\)

Chia 2 trường hợp:

+) T/h 1: \(x>2\) thì:

\(\left(1\right)\Leftrightarrow x-2+\frac{x-2}{x-2}=x-2+1=x-1\)

+) T/h 2: \(x< 2\) thì:

\(\left(1\right)\Leftrightarrow2-x+\frac{2-x}{x+2}=2-x-\frac{x-2}{x-2}=2-x-1=1-x\)