Question

rút gọn

a, \(x+3+\sqrt{x^2-6x+9}\) (x<=3)

b, \(\sqrt{x^2+4x+4}-\sqrt{x^2}\) (x-2<=x<=0)

c, \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\cdot\left(x-1\right)\)

d, \(\left|x-2\right|+\dfrac{\sqrt{x^2-4x+4}}{x-2}\) (x<2)

Answer 1

a/\(x+3+\sqrt{x^2-6x+9}=x+3+\sqrt{\left(x-3\right)^2}=x+3+\left|x-3\right|=x+3+3-x=6\)

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

c/ \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\cdot\left(x-1\right)=\sqrt{x^2-2x+1}=\sqrt{\left(x-1\right)^2}=\left|x-1\right|\)

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