How do I solve this, first I have to factor 2 x x − 1 + 3 x + 1 x − 1 − 1 + 9 x + 2 x 2 x 2 − 1 the solution is 3 x x + 1 The only advance that I have done is factor x 2 − 1= ( x − 1 ) ( x + 1 ) do not know how can I factor 1 + 9 x + 2 x 2 can someone please guide me in how to solve this exercise.

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How do I solve this, first I have to factor             2      x              x      −      1        +            3      x      +      1              x      −      1        −            1      +      9      x      +      2              x        2                            x        2            −      1      the solution is            3      x              x      +      1      The only advance that I have done is factor       x    2    −  1=  (  x  −  1  )  (  x  +  1  ) do not know how can I factor   1  +  9  x  +  2      x    2   can someone please guide me in how to solve this exercise.

Ethen Valentine · Accepted Answer

The first two terms are already over a common denominator.First simplify            2      x              x      −      1        +            3      x      +      1              x      −      1        −            1      +      9      x      +      2              x        2                            x        2            −      1        =            5      x      +      1              x      −      1        −            1      +      9      x      +      2              x        2                            x        2            −      1      Then put the first fraction over the same denominator as the second            (      5      x      +      1      )      (      x      +      1      )                      x        2            −      1        −            1      +      9      x      +      2              x        2                            x        2            −      1        =            (      5      x      +      1      )      (      x      +      1      )      −      (      1      +      9      x      +      2              x        2            )                      x        2            −      1      Now simplify the numerator

Petrovcic2x · Accepted Answer

Notice that      A    B    +            A      ′              B      C        =      C    C        A    B    +            A      ′              B      C        =            A      C      +              A        ′                    B      C      Then                                          (            x            +            1            )                                (            x            +            1            )                                                2            x                                (            x            −            1            )                          +                                          (            x            +            1            )                                (            x            +            1            )                                                3            x            +            1                                (            x            −            1            )                          +                              1            +            9            x            +            2                          x              2                                            (            x            −            1            )            (            x            +            1            )                                                            =                              2            x            (            x            +            1            )            +            (            3            x            +            1            )            (            x            +            1            )            −            (            1            +            9            x            +            2                          x              2                        )                                (            x            −            1            )            (            x            +            1            )                                                            =                              2                          x              2                        +            2            x            +            3                          x              2                        +            3            x            +            x            +            1            −            1            −            9            x            −            2                          x              2                                            (            x            −            1            )            (            x            +            1            )                                                            =                              3                          x              2                        −            3            x                                (            x            −            1            )            (            x            +            1            )

How do I solve this, first I have to factor 2 x </mrow> x

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