a: \(E=\left(\dfrac{x}{x-2}-\dfrac{3x-2}{x\left(x-2\right)}\right)\cdot\dfrac{x^2-4+4x-x^2}{x\left(x-2\right)}\)
\(=\dfrac{x^2-3x+2}{x\left(x-2\right)}\cdot\dfrac{4\left(x-1\right)}{x\left(x-2\right)}\)
\(=\dfrac{\left(x-1\right)}{x}\cdot\dfrac{4\left(x-1\right)}{x\left(x-2\right)}=\dfrac{4\left(x-1\right)^2}{x^2\left(x-2\right)}\)
b: Ta có: \(x^2-5x+6=0\)
=>(x-2)(x-3)=0
=>x=2(loại) hoặc x=3(nhận)
Thay x=3 vào E, ta được:
\(E=\dfrac{4\left(3-1\right)^2}{3^2\cdot\left(3-2\right)}=\dfrac{4\cdot2^2}{9}=\dfrac{16}{9}\)
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