How to simplify ( a 2 + a b + b 2 ) / ( a + a b + b )How can I simplify as much as possible: a 2 + a b + b 2 a + a b + b Also, first post here, looking forward to sticking around!

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How to simplify   (      a    2    +  a  b  +      b    2    )      /    (  a  +      a    b    +  b  )How can I simplify as much as possible:                    a        2            +      a      b      +              b        2                    a      +              a        b            +      b      Also, first post here, looking forward to sticking around!

Kaydence Washington · Accepted Answer

You could multiply by the conjugate of the denominator, then cancel.                                                        a              2                        +            a            b            +                          b              2                                            a            +                          a              b                        +            b                                              =                                            a              2                        +            a            b            +                          b              2                                            a            +            b            +                          a              b                                      ⋅                              a            +            b            −                          a              b                                            a            +            b            −                          a              b                                                                        =                              (                          a              2                        +            a            b            +                          b              2                        )            (            a            +            b            −                          a              b                        )                                (            a            +            b                          )              2                        −            a            b                                                            =                              (                          a              2                        +            a            b            +                          b              2                        )            (            a            +            b            −                          a              b                        )                                              a              2                        +            2            a            b            +                          b              2                        −            a            b                                                            =                              (                          a              2                        +            a            b            +                          b              2                        )            (            a            +            b            −                          a              b                        )                                              a              2                        +            a            b            +                          b              2                                                                        =        a        +        b        −                  a          b

varitero5w · Accepted Answer

a        2            +      a      b      +              b        2                    a      +              a        b            +      b        =            (              a        3            −              b        3            )              /            (      a      −      b      )              (              a                  3                      /                    2                    −              b                  3                      /                    2                    )              /            (              a                  1                      /                    2                    −              b                  1                      /                    2                    )        =                    a                  3                      /                    2                    +              b                  3                      /                    2                                    a                  1                      /                    2                    +              b                  1                      /                    2                      =  a  −      a    b    +  b

How to simplify ( a 2 </msup> + a b + b 2 </msup>

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