PreCalc 7/(3-2x) + 11/(3x+5) = (-5)/(2x-3)

[Guest]

7/(3-2x) + 11/(3x+5) = (-5)/(2x-3)

[Guest]

The equation is equivalent to:

7/(3-2x) + 11/(3x+5) = 5/(3 - 2x)

The least common denominator is (3 - 2x)(3x + 5)
so we multiply the both sides by (3 - 2x)(3x + 5)

[Guest]

(3 - 2x)(3x + 5) (7/(3-2x) + 11/(3x+5)) = (3 - 2x)(3x + 5)(5/(3 - 2x))
(3 - 2x)(3x + 5) * 7/(3-2x) + (3 - 2x)(3x + 5) * 11/(3x + 5) = 5(3x + 5)
7(3x + 5) + 11(3-2x) = 5(3x + 5)
7(3x + 5) - 5(3x+2) + 11(3-2x) = 0
2(3x + 5) + 11(3-2x)=0
6x + 10 + 33 - 22x = 0
-16x = - 43
x = 43/16