Rút gọn \(A=\sqrt{\frac{\left(2x-1\right)^4}{\left(3x-2\right)^2}}-\frac{4x^2-1}{3x-2}\) với \(x>\frac{2}{3}.\)
Hướng dẫn giải
Do \(x>\frac{2}{3}\) nên 3x - 2 > 0.
Ta có: \(A=\sqrt{\frac{\left(2x-1\right)^4}{\left(3x-2\right)^2}}-\frac{4x^2-1}{3x-2}=\frac{\sqrt{\left(2x-1\right)^4}}{\sqrt{\left(3x-2\right)^2}}-\frac{4x^2-1}{3x-2}\)
\(=\frac{\left(2x-1\right)^2}{\left|3x-2\right|}-\frac{4x^2-1}{3x-2}=\frac{4x^2-4x+1}{3x-2}-\frac{4x^2-1}{3x-2}\)
\(=\frac{4x^2-4x+1-4x^2+1}{3x-2}=\frac{2-4x}{3x-2}.\)
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