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Solve for $r$: $\frac{r+9}{r-3} = \frac{r-2}{r+5}$

Guest Dec 30, 2017

Best Answer 

 #1
avatar+5931 
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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

hectictar  Dec 30, 2017
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1+0 Answers

 #1
avatar+5931 
+1
Best Answer

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

 

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

hectictar  Dec 30, 2017

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