MHB How to simplify algebraic expression

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The discussion focuses on simplifying the algebraic expression \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}}. Participants confirm that the steps taken to simplify the expression are correct, leading to the final result of \frac{1}{2(x - 3)(x - 2)}. There is a consensus that no errors were made during the simplification process. The discussion emphasizes clarity in each transformation of the expression. Overall, the simplification appears accurate and well-validated by contributors.
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\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}}

\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \\<br /> \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(x - 2)^{2}} \\<br /> \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{\frac{1}{2}}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(x - 2)^{2}} \\<br /> \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(x - 2)^{2}} \\<br /> \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2(x - 2)^{2}} \\<br /> \frac{1}{(\frac{x - 3}{x - 2})} \cdot \frac{1}{2(x - 2)^{2}} \\<br /> \frac{1}{(x - 3)} \cdot \frac{1}{2(x - 2)} \\<br /> \frac{1}{2(x - 3)(x - 2)}

Which step have I done incorrectly?
 
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I don't see that you have done any step incorrectly! What makes you thing you have?
 
Can't find any errors, seems right.
 
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