Best way to simplify a polynomial fraction divided by a polynomial fraction as completely as possibleI've been trying for the past few days to complete this question from a review booklet before I start university:Simplify as completely as possible:( 5x^2 -9x -2 / 30x^3 + 6x^2 ) / ( x^4 -3x^2 -4 / 2x^8 +6x^7 + 4x^6 )However, I've only gotten as far as this answer below:( (x -1) / 6x^2 ) / ((x^2 +1)(x^2 -4) / (2x^4 +4x^3)(x^4 + x^3))I can't figure out how to simplify it further. What is the best / a good way to approach such a question that consists of a polynomial fraction divided by a polynomial fraction?Is it generally a good idea to factor each fraction first then multiply them like I attempted above, or is it better to multiply them without factoring then try to simplify one big fraction?

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Best way to simplify a polynomial fraction divided by a polynomial fraction as completely as possibleI&#039;ve been trying for the past few days to complete this question from a review booklet before I start university:Simplify as completely as possible:( 5x^2 -9x -2 / 30x^3 + 6x^2 ) / ( x^4 -3x^2 -4 / 2x^8 +6x^7 + 4x^6 )However, I&#039;ve only gotten as far as this answer below:( (x -1) / 6x^2 )   /   ((x^2 +1)(x^2 -4) / (2x^4 +4x^3)(x^4 + x^3))I can&#039;t figure out how to simplify it further. What is the best / a good way to approach such a question that consists of a polynomial fraction divided by a polynomial fraction?Is it generally a good idea to factor each fraction first then multiply them like I attempted above, or is it better to multiply them without factoring then try to simplify one big fraction?

Rayna Aguilar · Accepted Answer

5                          x              2                        −            9            x            −            2                                30                          x              3                        +            6                          x              2                                      ÷                                            x              4                        −            3                          x              2                        −            4                                2                          x              8                        +            6                          x              7                        +            4                          x              6                                                          =                                                  (            x            −            2            )            (            5            x            +            1            )                                6                          x              2                        (            5            x            +            1            )                          ×                              2                          x              6                        (            x            +            1            )            (            x            +            2            )                                (            x            −            2            )            (            x            +            2            )            (                          x              2                        +            1            )                                              =                                                                x              4                        (            x            +            1            )                                3            (                          x              2                        +            1            )

sombereki51 · Accepted Answer

simplifying we obtain            (      5              x        2            −      9      x      −      2      )      (      2              x        8            +      6              x        7            +      4              x        6            )              (      3              x        3            +      6              x        2            )      (              x        4            −      3              x        2            3      −      4      )      multiplying numerator and denominator out we obtain:            10                              x                          10                    +      12                              x                          9                    −      38                              x                          8                    −      48                              x                          7                    −      8                              x                          6                            3                              x                          7                    +      6                              x                          6                    −      9                              x                          5                    −      18                              x                          4                    −      12                              x                          3                    −      24                              x                          2

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