Question

what should be added to get (x - 1/x - 2) to obtain (2x² - 4/x² - 4)​

Answer 1

Step-by-step explanation:

Let the number be y.

(x - 1/x - 2) + y = (2x² - 4/x² - 4)

y = (2x² - 4/x² - 4) - (x - 1/x - 2)

= [(2x² - 4) - (x-1)(x+2)] / (x² - 4)

= [2x² - 4 - (x² - x + 2x - 2)] / (x² - 4)

= (2x² - 4 - x² + x - 2x + 2) / (x² - 4)

= (x² - x - 2) / (x² - 4)

(x² - x - 2) / (x² - 4) should be added to (x - 1/x - 2) to get (2x² - 4/x² - 4).