1.3 Simplify completely 1.3.1 \( x-3-\frac{5 x-6}{2-x}-\frac{4}{x-2} \)

Calculate or simplify the expression \( x-3-\frac{5x-6}{2-x}-\frac{4}{x-2} \). Simplify the expression by following steps: - step0: Solution: \(x-3-\frac{5x-6}{2-x}-\frac{4}{x-2}\) - step1: Reduce fractions to a common denominator: \(\frac{x\left(2-x\right)}{2-x}-\frac{3\left(2-x\right)}{2-x}-\frac{5x-6}{2-x}-\frac{4\left(-1\right)}{\left(x-2\right)\left(-1\right)}\) - step2: Reorder the terms: \(\frac{x\left(2-x\right)}{2-x}-\frac{3\left(2-x\right)}{2-x}-\frac{5x-6}{2-x}-\frac{4\left(-1\right)}{-\left(x-2\right)}\) - step3: Rewrite the expression: \(\frac{x\left(2-x\right)}{2-x}-\frac{3\left(2-x\right)}{2-x}-\frac{5x-6}{2-x}-\frac{4\left(-1\right)}{2-x}\) - step4: Transform the expression: \(\frac{x\left(2-x\right)-3\left(2-x\right)-\left(5x-6\right)-4\left(-1\right)}{2-x}\) - step5: Multiply the terms: \(\frac{2x-x^{2}-3\left(2-x\right)-\left(5x-6\right)-4\left(-1\right)}{2-x}\) - step6: Multiply the terms: \(\frac{2x-x^{2}-\left(6-3x\right)-\left(5x-6\right)-4\left(-1\right)}{2-x}\) - step7: Rewrite the expression: \(\frac{2x-x^{2}-\left(6-3x\right)-\left(5x-6\right)-\left(-4\right)}{2-x}\) - step8: Subtract the terms: \(\frac{-x^{2}+4}{2-x}\) - step9: Calculate: \(\frac{\left(2-x\right)\left(2+x\right)}{2-x}\) - step10: Reduce the fraction: \(2+x\) The simplified expression is \(2+x\).