a. x +3 + √x^2 – 6x +9 (x ≤ 3) b. √x^2 + 4x +4 – √x^2 (-2 ≤ x ≤ 0)

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1. a. x +3 + $\sqrt[]{x^2 – 6x +9}$ (x ≤ 3)

   = x + 3 + $\sqrt[]{(x-3)²}$

   = x + 3 + x – 3

   = 2x

   b. √(x^2 + 4x +4) – √x^2 (-2 ≤ x ≤ 0)                 

   = √( x +2)² – √x^2

   = x+2 – x

   = 2

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2. `a. x +3 + sqrt(x^2 – 6x +9 )(x ≤ 3)`

   `=x+3+sqrt((x-3)^2)`

   `=x+3+x-3`

   `=2x`

   `b. sqrt(x^2 + 4x +4 )- sqrt(x^2 )(-2 ≤ x ≤ 0)`

   `=sqrt((x+2)^2)-x`

   `=x+2-x`

   `=2`

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