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\(\frac{r+9}{r-3}\,=\,\frac{r-2}{r+5}\)

 

Note that  r  cannot be  3  or  -5  since these values cause a zero in the denominator of the original equation. Now multiply both sides of the equation by  r - 3 , and multiply both sides by  r + 5 .

 

(r + 9)(r + 5)  =  (r - 2)(r - 3)

                                                  Multiply out the factors.

r² + 14r + 45   =   r² - 5r + 6

                                                  Subtract  r²  from both sides of the equation.

14r + 45  =  -5r + 6

                                                  Add  5r  to both sides.

19r + 45  =  6

                                                  Subtract  45  from both sides.

19r  =  -39

                                                  Divide both sides by  19 .

r  =  -39/19