Distributing multiplication of rational functionsI am having trouble distributing with fractions. This ( 1 ( x + 3 ) + ( x + 3 ) ( x − 3 ) ) ( 9 − x 2 ) = − ( x 2 − 3 ) 9 − x 2 ( 9 − x 2 )has the answer { [ x = − 9 7 ] } I start solving by cancelling ( 9 − x 2 ) on the right hand side, and multiplying ( 9 − x 2 ) with the terms on the left hand side by foiling (multiplying term by term). So the first step is 9 × 1 x + 3 + 9 ( x + 3 ) x − 3 − x 2 × 1 x + 3 − x 2 ( x + 3 ) x − 3 = − x 2 − 3This is apparently wrong because it has another answer, { [ x = − 3 7 ] } What am I doing wrong?

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Distributing multiplication of rational functionsI am having trouble distributing with fractions. This      (          1              (        x        +        3        )              +                  (        x        +        3        )                    (        x        −        3        )              )      (  9  −      x    2    )  =  −            (              x        2            −      3      )              9      −              x        2              (  9  −      x    2    )has the answer       {          [      x      =      −              9        7            ]        }  I start solving by cancelling   (  9  −      x    2    ) on the right hand side, and multiplying   (  9  −      x    2    ) with the terms on the left hand side by foiling (multiplying term by term). So the first step is  9  ×      1          x      +      3        +            9      (      x      +      3      )              x      −      3        −      x    2    ×      1          x      +      3        −                    x        2            (      x      +      3      )              x      −      3        =  −      x    2    −  3This is apparently wrong because it has another answer,       {          [      x      =      −              3        7            ]        }   What am I doing wrong?

Kumamotors · Accepted Answer

Cancelling   (  9  −      x    2    ) on the RHS leaves you with   −  (      x    2    −  3  ). Next I&#039;d recommend finding a common denominator and combining the fractions inside the parentheses on the LHS. You should get      1          (      x      +      3      )        +            (      x      +      3      )              (      x      −      3      )        =            x      −      3      +      (      x      +      3              )        2                            x        2            −      9      which means the LHS will simplify to   −  (  x  −  3  +  (  x  +  3      )    2    ), leaving you with  −  (  x  −  3  +  (  x  +  3      )    2    )  =  −  (      x    2    −  3  )Can you take it from here? If I carry out the rest of this algebra I find that   x  =            −      9        7

kunyatia33 · Accepted Answer

(          1              x        +        3              +                  x        +        3                    x        −        3              )    (  9  −      x    2    )  −      x    2    −  3It will be            9      −              x        2                    x      +      3        +            (      x      +      3      )      (      9      −              x        2            )              x      −      3        =  −      x    2    −  3after that            (      9      −              x        2            )      (      x      −      3      )              (      x      +      3      )      (      x      −      3      )        +            (      x      +      3      )      (      x      +      3      )      (      9      −              x        2            )              (      x      −      3      )      (      x      +      3      )        =  −      x    2    −  3Note that   9  −      x    2    =  −  (      x    2    −  9  )  =  −  (  x  +  3  )  (  x  −  3  ), i.e., you can cancel it with the denominator

Distributing multiplication of rational functions I am having trouble distributing with fractions.

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