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

Dec 30, 2017

#1
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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

19r + 45  =  6

Subtract  45  from both sides.

19r  =  -39

Divide both sides by  19 .

r  =  -39/19

Dec 30, 2017

#1
+8437
+1

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

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

19r + 45  =  6

Subtract  45  from both sides.

19r  =  -39

Divide both sides by  19 .

r  =  -39/19

hectictar Dec 30, 2017