How is this equation true?I was looking through my notes when I stumbled upon this eqation: n 2 + n − n = ( n 2 + n ) − n 2 n 2 + n + n I was trying to make sense of it, but I didnt succeed.Can you give me a hint or tell me how this tranformation is called ?

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How is this equation true?I was looking through my notes when I stumbled upon this eqation:            n      2        +    n    −  n  =            (              n        2            +      n      )      −              n        2                                      n          2                +        n            +      n      I was trying to make sense of it, but I didnt succeed.Can you give me a hint or tell me how this tranformation is called ?

muilasqk · Accepted Answer

Multiply             n      2        +    n    +  n top and bottom. In other words, we have:            n      2        +    n    −  n  =            (                        n          2                +        n            −      n      )      ×      (                        n          2                +        n            +      n      )                                n          2                +        n            +      n      I think the rest you can figure it out on your own. We usually call such a method as &#039;rationalizing&#039; the surd.

fermetrakr · Accepted Answer

If you must find the limit of            n      2        +    n    −  n  ;    n  →  ∞You get an indeterminate form. Thus you multiply by             n      2        +    n    +  n the numerator and the denominator                    (                  n          2                +        n        )        −                  n          2                                                  n            2                    +          n                +        n              =            n                                    n            2                    +          n                +        n              =            n              n                  1          +                      1            n                          +        n              =            n              n                  (                      1            +                          1              n                                +          1          )                      =            1                        1          +                      1            n                          +        1              =            1      2      Hope this helps to recall the reason why you wrote down this note :)

How is this equation true? I was looking through my notes when I stumbled upon this eqation: sqrt(n^2 +n) -n = ((n^2 +n) - n^2)/(sqrt(n^2 +n) +n) I was trying to make sense of it, but I didnt succeed. Can you give me a hint or tell me how this tranformation is called ?

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