Get rid of the square roots of the denominator: 1 7 − 2 5 + 3 I squared the whole denominator, but that didn't help.Also I searched for a propriety or identity like A 2 − B 2 , but I didn't see one that could fit. Any help is appreciated.

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Get rid of the square roots of the denominator:             1                        7                −        2                  5                +                  3                     I squared the whole denominator, but that didn&#039;t help.Also I searched for a propriety or identity like       A    2    −      B    2  , but I didn&#039;t see one that could fit. Any help is appreciated.

iskakanjulc · Accepted Answer

1                                    7                        −            2                          5                        +                          3                                                          =                  1                                    7                        −            2                          5                        +                          3                                      ⋅                                            7                        −            2                          5                        −                          3                                                          7                        −            2                          5                        −                          3                                                                        =                                            7                        −            2                          5                        −                          3                                            (                          7                        −            2                          5                                      )              2                        −            3                                                            =                                            7                        −            2                          5                        −                          3                                            4            (            6            −                          35                        )                          ⋅                              6            +                          35                                            6            +                          35                                                                        =                              (                          7                        −            2                          5                        −                          3                        )            (            6            +                          35                        )                    4

tripes3h · Accepted Answer

To get rid of the square roots of the denominator, you may use       a    2    −      b    2    =  (  a  +  b  )  (  a  −  b  )            1                        7                −        2                  5                +                  3                        =                              7                −        2                  5                −                  3                            (                  7                −        2                  5                          )          2                −        3                =                              7                −        2                  5                −                  3                            7        −        4                  35                +        20        −        3                =                              7                −        2                  5                −                  3                            24        −        4                  35                        =                    (                  7                −        2                  5                −                  3                )        (        24        +        4                  35                )                              24          2                −        16        ∗        35                =                    (                  7                −        2                  5                −                  3                )        (        24        +        4                  35                )            16          =                    −        24                  3                −        20                  5                −        16                  7                −        4                  105                    16          =                    −        6                  3                −        5                  5                −        4                  7                −                  105                    4

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