द) \( \left(\frac{2}{x}+\frac{x}{2}-2\right) \cdot \frac{4 x^{2}+8 x}{x^{2}-4} \)

Calculate or simplify the expression \( (2/x+x/2-2) * (4*x^2+8*x)/(x^2-4) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(\frac{2}{x}+\frac{x}{2}-2\right)\left(4x^{2}+8x\right)}{\left(x^{2}-4\right)}\) - step1: Remove the parentheses: \(\frac{\left(\frac{2}{x}+\frac{x}{2}-2\right)\left(4x^{2}+8x\right)}{x^{2}-4}\) - step2: Calculate: \(\frac{\frac{4+x^{2}-4x}{2x}\times \left(4x^{2}+8x\right)}{x^{2}-4}\) - step3: Multiply the terms: \(\frac{\left(4+x^{2}-4x\right)\left(2x+4\right)}{x^{2}-4}\) - step4: Factor the expression: \(\frac{\left(x-2\right)^{2}\left(2x+4\right)}{\left(x-2\right)\left(x+2\right)}\) - step5: Reduce the fraction: \(\frac{\left(x-2\right)\left(2x+4\right)}{x+2}\) - step6: Factor the expression: \(\frac{\left(x-2\right)\times 2\left(x+2\right)}{x+2}\) - step7: Reduce the fraction: \(\left(x-2\right)\times 2\) - step8: Calculate: \(2\left(x-2\right)\) - step9: Rearrange the terms: \(2x-4\) La expresión dada se simplifica a \(2x-4\).