\(\dfrac{a^3-3a+2}{2a^3-7a^2+8a-3}\)
\(=\dfrac{a^3-a-2a+2}{2a^3-2a^2-5a^2+5a+3a-3}\)
\(=\dfrac{a\left(a-1\right)\left(a+1\right)-2\left(a-1\right)}{2a^2\left(a-1\right)-5a\left(a-1\right)+3\left(a-1\right)}\)
\(=\dfrac{\left(a-1\right)\left(a^2+a-2\right)}{\left(a-1\right)\left(2a^2-5a+3\right)}\)
\(=\dfrac{\left(a+2\right)\left(a-1\right)}{\left(a-1\right)\left(2a-3\right)}\)
\(=\dfrac{a+2}{2a-3}\)
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