How to simplify 3 x 2 + 5 x − 2 6 x 3 − 17 x 2 − 4 x + 3 ?I'm given this algebraic fraction, and I'm asked to simplify it as much as possible: 3 x 2 + 5 x − 2 6 x 3 − 17 x 2 − 4 x + 3 I applied Ruffini's Rule to find the roots of both the Numerator and Denominator. This helped me simplify the fraction to: ( x + 2 ) ( 3 x − 1 ) ( x − 3 ) ( 6 x 2 + x − 1 ) I tried to further simplify the factor ( 6 x 2 + x − 1 ), to no avail. I tried these two techniques:1. I tried to find any possible roots, but neither ( x − 1 ) nor ( x + 1 ) are roots.2. I tried to see if that is a perfect square in the form: ( x + a ) 2 , but it isn't.I'm not aware of any other way/technique that helps me simplify that expression. I'd just need a bit of your help. Thanks!

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How to simplify             3              x        2            +      5      x      −      2              6              x        3            −      17              x        2            −      4      x      +      3      ?I&#039;m given this algebraic fraction, and I&#039;m asked to simplify it as much as possible:                    3                  x          2                +        5        x        −        2                    6                  x          3                −        17                  x          2                −        4        x        +        3            I applied Ruffini&#039;s Rule to find the roots of both the Numerator and Denominator. This helped me simplify the fraction to:                    (        x        +        2        )        (        3        x        −        1        )                    (        x        −        3        )        (        6                  x          2                +        x        −        1        )            I tried to further simplify the factor   (  6      x    2    +  x  −  1  ), to no avail. I tried these two techniques:1. I tried to find any possible roots, but neither   (  x  −  1  ) nor   (  x  +  1  ) are roots.2. I tried to see if that is a perfect square in the form:   (  x  +  a      )    2  , but it isn&#039;t.I&#039;m not aware of any other way/technique that helps me simplify that expression. I&#039;d just need a bit of your help. Thanks!

Phoenix Morse · Accepted Answer

The factors that will allow you to simplify this fraction comes from the expression   6      x    2    +  x  −  1, and in order to factor this, you can do the following:consider pairs of   x-coefficients that will multiply to give   −  6 and add to give   1. The pair that should catch your eye is   3 and   −  2. Using this, the expression now becomes:   6      x    2    +  3  x  −  2  x  −  1 which allows you to factor out two brackets independently like so:  3  x  (  2  x  +  1  )  −  1  (  2  x  +  1  )  (  3  x  −  1  )  (  2  x  +  1  )hence your fraction becomes:            (      x      +      2      )      (      3      x      −      1      )              (      x      −      3      )      (      3      x      −      1      )      (      2      x      +      1      )      can you simplify this?

ye1neh4 · Accepted Answer

It is possible to factor   6      x    2    +  x  −  1. First, we look for two numbers whose sum is 1 and whose product is −6. (In general, for   a      x    2    +  b  x  +  c, we would seek two numbers with sum b and product ac.) We find these numbers to be 3 and −2. We now &quot;split the middle term&quot;, replacing &quot;  +  x&quot; with &quot;  +  3  x  −  2  x&quot;:  6      x    2    +  3  x  −  2  x  −  1The resulting expression we can &quot;factor by grouping&quot;:                    6                  x          2                +        3        x        −        2        x        −        1                            =        3        x        (        2        x        +        1        )        −        1        (        2        x        +        1        )                                          =        (        3        x        −        1        )        (        2        x        +        1        )            Applying this factorization, you see that your denominator now has a common factor with the numerator, which can be canceled.

How to simplify (3x^2+5x-2)/(6x^3-17x^2-4x+3)? I'm given this algebraic fraction, and I'm asked to simplify it as much as possible: (3x^2+5x-2)/(6x^3-17x^2-4x+3)

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