Adding fractions with variables and using common denominator? Rather basic math, but here I am..So I have these fractions I need to merge together and shorten: 1 2 a + 8 + 4 a 2 − 16 + 4 a − 4 I understand that I need to make the denominators the same so that I can merge these fractions together, but I have no idea how.I assume I need to find the common denominator, which is a friend told me was 2 a 2 − 64. I don't know what to do from here, please help?How do I use the common denominator to make these denominators the same?EDIT: Okay so I failed miserably at this MathJax thing. What I am trying to say is: 1 2 a + 8 + 4 a 2 − 16 + 4 a − 4 A quick lesson in writing fractions on this forum would also be immensely appreciated.

Question

Adding fractions with variables and using common denominator? Rather basic math, but here I am..So I have these fractions I need to merge together and shorten:      1          2      a      +      8        +      4                  a        2            −      16        +      4          a      −      4      I understand that I need to make the denominators the same so that I can merge these fractions together, but I have no idea how.I assume I need to find the common denominator, which is a friend told me was   2      a    2    −  64. I don&#039;t know what to do from here, please help?How do I use the common denominator to make these denominators the same?EDIT: Okay so I failed miserably at this MathJax thing. What I am trying to say is:      1          2      a      +      8        +      4                  a        2            −      16        +      4          a      −      4      A quick lesson in writing fractions on this forum would also be immensely appreciated.

Ronnie Glenn · Accepted Answer

Consider that this expression can be rewritten as:      1          2      a      +      8        +      4                  a        2            −      16        +      4          a      −      4        =      1          2      (      a      +      4      )        +      4                  a        2            −      16        +      4          a      −      4      Now   (  a  +  4  )  (  a  −  4  )  =      a    2    −  16, so multiply fractions by clever forms of one:      1          2      (      a      +      4      )                  (      a      −      4      )              (      a      −      4      )        +      4                  a        2            −      16            2    2    +      4          a      −      4                  2      (      a      +      4      )              2      (      a      +      4      )        =            (      a      −      4      )              2      (              a        2            −      16      )        +      8          2      (              a        2            −      16      )        +            8      (      a      +      4      )              2      (              a        2            −      16      )      Now, we can simply add up fractions:                                          (            a            −            4            )                                2            (                          a              2                        −            16            )                          +                  8                      2            (                          a              2                        −            16            )                          +                              8            (            a            +            4            )                                2            (                          a              2                        −            16            )                                              =                              8            a            +            32            +            8            +            a            −            4                                2            (                          a              2                        −            16            )                                                                          =                              9            a            +            36                                2            (                          a              2                        −            16            )                                                                          =                              9            (            a            +            4            )                                2            (            a            +            4            )            (            a            −            4            )                                                                          =                  9                      2            (            a            −            4            )

Adding fractions with variables and using common denominator? Rather basic math, but here I am.. So

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