y+(2)/(3)=(2y-12)/(3y-9)

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Solution for y+(2)/(3)=(2y-12)/(3y-9) equation:


D( y )

3*y-9 = 0

3*y-9 = 0

3*y-9 = 0

3*y-9 = 0 // + 9

3*y = 9 // : 3

y = 9/3

y = 3

y in (-oo:3) U (3:+oo)

y+2/3 = (2*y-12)/(3*y-9) // - (2*y-12)/(3*y-9)

y-((2*y-12)/(3*y-9))+2/3 = 0

(-1*(2*y-12))/(3*y-9)+y+2/3 = 0

(-1*3*(2*y-12))/(3*(3*y-9))+(3*y*(3*y-9))/(3*(3*y-9))+(2*(3*y-9))/(3*(3*y-9)) = 0

3*y*(3*y-9)-1*3*(2*y-12)+2*(3*y-9) = 0

9*y^2-33*y+6*y-18+36 = 0

9*y^2-27*y+18 = 0

9*y^2-27*y+18 = 0

9*(y^2-3*y+2) = 0

y^2-3*y+2 = 0

DELTA = (-3)^2-(1*2*4)

DELTA = 1

DELTA > 0

y = (1^(1/2)+3)/(1*2) or y = (3-1^(1/2))/(1*2)

y = 2 or y = 1

9*(y-1)*(y-2) = 0

(9*(y-1)*(y-2))/(3*(3*y-9)) = 0

(9*(y-1)*(y-2))/(3*(3*y-9)) = 0 // * 3*(3*y-9)

9*(y-1)*(y-2) = 0

( y-1 )

y-1 = 0 // + 1

y = 1

( y-2 )

y-2 = 0 // + 2

y = 2

y in { 1, 2 }

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