Question

[Tô Thu Huyền]

Rút gọn các biểu thức sau:

a. x+3+ \(\sqrt{x^2-6x+9}\) (x ≤ 3)

b. \(\sqrt{x^2+4x+4}-\sqrt{x^2}\) ( -2 ≤ x ≤ 0 )

c. \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\) ( x > 1)

d. /x-2/ + \(\dfrac{\sqrt{x^2-4x+4}}{x-2}\) ( x < 2)

Answer 1

[Phùng Khánh Linh]

\(a.x+3+\sqrt{x^2-6x+9}=x+3+\text{ |}x-3\text{ |}=x+3+3-x=6\) \(b.\sqrt{x^2+4x+4}-\sqrt{x^2}=\text{ |}x+2\text{ |}-\text{ |}x\text{ |}=x+2-\left(-x\right)=x+2+x=2x+2\) \(c.\dfrac{\sqrt{x^2-2x+1}}{x-1}=\dfrac{x-1}{x-1}=1\)

\(d.\text{ |}x-2\text{ |}+\dfrac{\sqrt{x^2-4x+4}}{x-2}=\text{ |}x-2\text{ |}+\dfrac{\text{ |}x-2\text{ |}}{x-2}=2-x+\dfrac{-\left(x-2\right)}{x-2}=2-x-1=1-x\)