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

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UpStudy AI · Accepted Answer

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:
  $$\frac{\left(\frac{2}{x}+\frac{x}{2}-2ight)\left(4x^{2}+8xight)}{\left(x^{2}-4ight)}$$
- step1: Remove the parentheses:
  $$\frac{\left(\frac{2}{x}+\frac{x}{2}-2ight)\left(4x^{2}+8xight)}{x^{2}-4}$$
- step2: Calculate:
  $$\frac{\frac{4+x^{2}-4x}{2x}	imes \left(4x^{2}+8xight)}{x^{2}-4}$$
- step3: Multiply the terms:
  $$\frac{\left(4+x^{2}-4xight)\left(2x+4ight)}{x^{2}-4}$$
- step4: Factor the expression:
  $$\frac{\left(x-2ight)^{2}\left(2x+4ight)}{\left(x-2ight)\left(x+2ight)}$$
- step5: Reduce the fraction:
  $$\frac{\left(x-2ight)\left(2x+4ight)}{x+2}$$
- step6: Factor the expression:
  $$\frac{\left(x-2ight)	imes 2\left(x+2ight)}{x+2}$$
- step7: Reduce the fraction:
  $$\left(x-2ight)	imes 2$$
- step8: Calculate:
  $$2\left(x-2ight)$$
- step9: Rearrange the terms:
  $$2x-4$$
La expresión dada se simplifica a $$2x-4$$.
$$2x - 4$$

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