divide these rational expressions

Question

(6x^2 -3x+5) /(2x-3)

Answer 1

Use long division.  Divide the same way you divide regular numbers.

 

 

                       3x + 3

             _____________

(2x - 3) | 6x² - 3x + 5

              6x² - 9x

             _____________

                      6x + 5

                      6x - 9

                     ______

                            14

 

 

Quotient = 3x + 3

Remainder = 14

 

If you want to check, multiply the quotient by the divisor.  Then add the remainder to the result.  We would get back the dividend.

 

(3x + 3)(2x - 3) + 14 = (6x² - 9x + 6x - 9) + 14

                                = 6x² - 3x + 5