Simplifying fraction with square root as denominatorI'm trying to find the integral of: 2 x − 3 x + x 2 x but I first need to simplify it so I tried dividing by the x for each of the numbers on the top like so: 2 x x and did the same for the others. For the one above it was easy to see that it just simplifies to 2. But I am unsure how to do the same for the others for instance − 3 x x I know to − x but i don't know what − 3 x − x would come out with?

Question

Simplifying fraction with square root as denominatorI&#039;m trying to find the integral of:                    2                  x                −        3        x        +                  x          2                            x            but I first need to simplify it so I tried dividing by the       x   for each of the numbers on the top like so:                    2                  x                            x            and did the same for the others. For the one above it was easy to see that it just simplifies to 2. But I am unsure how to do the same for the others for instance                     −        3        x                    x              I know to   −      x   but i don&#039;t know what   −  3  x  −      x   would come out with?

Janiyah Patton · Accepted Answer

HINT :Rewrite                    2                  x                −        3        x        +                  x          2                            x              =                    2                  x                −        3                  x                          x                +        x        ⋅        x                    x              =                    2                  x                −        3                  x                          x                +                  x                          x                ⋅        x                    x            or                    2                  x                −        3        x        +                  x          2                            x              =                    2                  x                                                    1                2                                                    −        3                  x          1                +                  x          2                            x                                            1              2                                            ,where   x  =      x        x   and       x    =      x                            1          2

Ayaan Barr · Accepted Answer

Hint:            2              x            −      3      x      +              x        2                    x        =  2  −  3      x    +      x          3              /            2