Simplify x + 3 x − 6 − 2 x + 3 x − 6 + 8 How would I simplify this complex fraction? I know what the answer is, but I am just not sure how they got there.I have tried multiplying both sides by ( x − 6 ) but I am getting x 2 − 3 x − 18? Any ideas?

Question

Simplify                     x        +        3                    x        −        6        −        2                            x        +        3                    x        −        6        +        8            How would I simplify this complex fraction? I know what the answer is, but I am just not sure how they got there.I have tried multiplying both sides by   (  x  −  6  ) but I am getting       x    2    −  3  x  −  18? Any ideas?

trantegisis · Accepted Answer

x        +        3                    x        −        6        −        2                            x        +        3                    x        −        6        +        8              =            x      +      3              x      −      6      −      2        ⋅      1                  x        +        3                    x        −        6        +        8              =            x      +      3              x      −      8        ⋅      1                  x        +        3                    x        +        2              =            x      +      3              x      −      8        ⋅            x      +      2              x      +      3        =            x      +      2              x      −      8        .

Janet Forbes · Accepted Answer

Note that dividing by a fraction is equivalent to multiplying by its reciprocal -- hence this might be the first thing you want to do, so that you only have one numerator and denominator:                    x        +        3                    x        −        6        −        2                            x        +        3                    x        −        6        +        8              =            x      +      3              x      −      6      −      2        ⋅            (                        x          +          3                          x          −          6          +          8                    )              −      1        =            x      +      3              x      −      6      −      2        ⋅            x      −      6      +      8              x      +      3        =            (      x      +      3      )      (      x      −      6      +      8      )              (      x      −      6      −      2      )      (      x      +      3      )      Written like this, it is easier to see that the   x  +  3 terms cancel:  =            x      −      6      +      8              x      −      6      −      2        =            x      +      2              x      −      8

Simplify x + 3 </mrow> x

Answered question

Answer & Explanation

New Questions in Pre-Algebra