Express  ` (7x+3)/(x-1)`  in the form `A + B/(x-1)` , where A and B are constants.   Thanks!

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To express the given rational expression in the form A + B/(x-1), divide the numerator by the denominator using long division.

   ` x - 1 | bar(7x+3) `  

The steps are:

> Divide 7x by x.  `(7x)/x=7`

   Write the 7 at the top of 7x.

> Then, multiply the resulting value by x-1. `7(x-1)=7x-7`

    Write this below 7x + 3.

> Next, subtract this from 7x+3. `7x+3-(7x-7)=11`

   Since 11 has no x, this is the remainder. 

> And, express the remainder as a fraction and add it to 7.

             `7 `    

  `x - 1 | bar(7x+3) `                

     `(-)` `7x - 7`

         `-----`

                  `11`


Hence,  `(7x+3)/(x-1) = 7 + 11/(x-1)` .

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