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# (r-2)/(r+2)-2r/(r+9)=6?

(r-2)/(r+2)-2r/(r+9)=6

Simplify that to a rational fraction. Please explain the steps. ^_^

### 1 Answer

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- Anonymous1 decade agoFavorite Answer
[(r-2)(r+9) -2r(r+2)] / [(r+2)(r+9)] = 6

(r^2 + 7r -18 -2r^2 - 4r) / [(r+2)(r+9)] = 6

(-r^2 + 3r - 18) / (r^2 + 11r + 18) = 6

-r^2 + 3r - 18 = 6(r^2 + 11r + 18) = 6r^2 + 66r + 108

7r^2 + 63r + 126 = 0

(7r + 42)(r+3) = 0

r = -6; r = -3

Using r = -6:

(-8/-4) - (-12/3) = 6 ==> 2/1 + 4/1 = 6

Using r = -3

(-5/-1) - (-6/6) = 6 ==> 5/1 + 1/1 = 6

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