algebra exponents and fractionsI could be over thinking or tired... But I am to embarrassed to ask my prof. this probably very simple algebra rule I am ignorant of... Also this is just a snip-it from a inductive proof example.Say you have something like this 4 k − 1 3 + 3 ∗ 4 k 3 = 4 ∗ 4 k − 1 3 My question is what algebra rules or rules of fractions allow this? In other words what computation is going on? I can agree that the 3 should cancel out 3 ∗ 4 k 3 = 4 k But wouldn't that mean it be something like this ( 4 k − 1 ) ∗ 4 k 3 or more accurately ( 4 k − 1 ) 3 ∗ 4 k and not this? 4 ∗ 4 k − 1 3

Question

algebra exponents and fractionsI could be over thinking or tired... But I am to embarrassed to ask my prof. this probably very simple algebra rule I am ignorant of... Also this is just a snip-it from a inductive proof example.Say you have something like this                              4          k                −        1            3        +                    3        ∗                  4          k                    3        =                    4        ∗                  4          k                −        1            3      My question is what algebra rules or rules of fractions allow this? In other words what computation is going on? I can agree that the 3 should cancel out                    3        ∗                  4          k                    3        =                      4        k            But wouldn&#039;t that mean it be something like this                    (                  4          k                −        1        )        ∗                  4          k                    3      or more accurately                    (                  4          k                −        1        )            3              ∗              4        k            and not this?                    4        ∗                  4          k                −        1            3

jugf5 · Accepted Answer

4          k                −        1            3        +                    3        ⋅                  4          k                    3           these fractions have the same denominator so we can write the fraction as one now                       4        k            −      1      +      3      ⋅              4        k              3       recall   u  +  3  u  =  4  u     so we have                       4        k            (      1      +      3      )      −      1        3    =                    4        k            (      4      )      −      1        3    =            4      ⋅              4        k            −      1        3    =                    4                  k          +          1                    −      1        3