x²- 4 + 4/x²
Factorise using identities.
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We have,
![\quad \: {x}^{2} - 4 + \frac{4}{ {x}^{2} } \\ \\ = {(x)}^{2} - 2(x) \left( \frac{2}{x} \right) + { \left( \frac{2}{x} \right)}^{2} \\ \\ = { \left( x - \frac{2}{x} \right)}^{2} \\ \\ = { \left( \frac{ {x}^{2} - 2}{x} \right)}^{2} \quad \: {x}^{2} - 4 + \frac{4}{ {x}^{2} } \\ \\ = {(x)}^{2} - 2(x) \left( \frac{2}{x} \right) + { \left( \frac{2}{x} \right)}^{2} \\ \\ = { \left( x - \frac{2}{x} \right)}^{2} \\ \\ = { \left( \frac{ {x}^{2} - 2}{x} \right)}^{2}](https://tex.z-dn.net/?f=+%5Cquad+%5C%3A++%7Bx%7D%5E%7B2%7D++-+4+%2B++%5Cfrac%7B4%7D%7B+%7Bx%7D%5E%7B2%7D+%7D++%5C%5C++%5C%5C++%3D++%7B%28x%29%7D%5E%7B2%7D++-+2%28x%29+%5Cleft%28++%5Cfrac%7B2%7D%7Bx%7D+%5Cright%29+%2B++%7B+%5Cleft%28++%5Cfrac%7B2%7D%7Bx%7D+%5Cright%29%7D%5E%7B2%7D++%5C%5C++%5C%5C++%3D++%7B+%5Cleft%28+x+-++%5Cfrac%7B2%7D%7Bx%7D+%5Cright%29%7D%5E%7B2%7D++%5C%5C++%5C%5C++%3D++%7B+%5Cleft%28++%5Cfrac%7B+%7Bx%7D%5E%7B2%7D++-+2%7D%7Bx%7D+%5Cright%29%7D%5E%7B2%7D+)
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