\( \frac{10 x^{2}+9 x+2}{3 x-3} \cdot \frac{x-1}{2 x^{2}-5 x-3} \) Simplify your answer as much as possible.

Calculate or simplify the expression \( (10x^2+9x+2)/(3x-3) * (x-1)/(2x^2-5x-3) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\frac{\left(10x^{2}+9x+2\right)}{\left(3x-3\right)}\times \left(x-1\right)}{\left(2x^{2}-5x-3\right)}\) - step1: Remove the parentheses: \(\frac{\frac{10x^{2}+9x+2}{3x-3}\times \left(x-1\right)}{2x^{2}-5x-3}\) - step2: Multiply the terms: \(\frac{\frac{10x^{2}+9x+2}{3}}{2x^{2}-5x-3}\) - step3: Multiply by the reciprocal: \(\frac{10x^{2}+9x+2}{3}\times \frac{1}{2x^{2}-5x-3}\) - step4: Rewrite the expression: \(\frac{\left(2x+1\right)\left(5x+2\right)}{3}\times \frac{1}{\left(2x+1\right)\left(x-3\right)}\) - step5: Reduce the fraction: \(\frac{5x+2}{3}\times \frac{1}{x-3}\) - step6: Multiply the terms: \(\frac{5x+2}{3\left(x-3\right)}\) - step7: Simplify: \(\frac{5x+2}{3x-9}\) The simplified form of the expression \( \frac{10x^{2}+9x+2}{3x-3} \cdot \frac{x-1}{2x^{2}-5x-3} \) is \( \frac{5x+2}{3x-9} \).