[tex]1 - \frac{x + 2}{x - 2} [/tex][tex]x - 1 - \frac{3}{x - 3} [/tex][tex]x - \frac{1}{x - 2} - \frac{2x}{2 - x} [/tex]

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To simplify these expressions, we need to find a common denominator.

For the first expression, the common denominator is (x - 2). So, we rewrite the expression as:

[tex]\frac{(x - 2) - (x + 2)}{x - 2} [/tex]
[tex]\frac{x - 2 - x - 2}{x - 2} [/tex]
[tex]\frac{-4}{x - 2} [/tex]

For the second expression, the common denominator is (x - 3). So, we rewrite the expression as:

[tex]\frac{(x - 3)(x - 1) - 3x}{x - 3} [/tex]
[tex]\frac{x^2 - 3x - x + 3 - 3x}{x - 3} [/tex]
[tex]\frac{x^2 - 7x + 3}{x - 3} [/tex]

For the third expression, the common denominator is (x - 2)(2 - x). So, we rewrite the expression as:

[tex]\frac{(x - 2)(2 - x) - (1)(2 - x) - (2x)(x - 2)}{(x - 2)(2 - x)} [/tex]
[tex]\frac{2x - 4 - 2 + x - 2x}{(x - 2)(2 - x)} [/tex]
[tex]\frac{-3}{(x - 2)(2 - x)} [/tex]