9/(3x-9)=8/7+4/(x-3)

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Solution for 9/(3x-9)=8/7+4/(x-3) equation: 


D( x )

x-3 = 0

3*x-9 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

3*x-9 = 0

3*x-9 = 0

3*x-9 = 0 // + 9

3*x = 9 // : 3

x = 9/3

x = 3

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

9/(3*x-9) = 4/(x-3)+8/7 // - 4/(x-3)+8/7

9/(3*x-9)-(4/(x-3))-(8/7) = 0

9/(3*x-9)-4*(x-3)^-1-8/7 = 0

9/(3*x-9)-4/(x-3)-8/7 = 0

(7*9*(x-3))/(7*(3*x-9)*(x-3))+(-4*7*(3*x-9))/(7*(3*x-9)*(x-3))+(-8*(3*x-9)*(x-3))/(7*(3*x-9)*(x-3)) = 0

7*9*(x-3)-4*7*(3*x-9)-8*(3*x-9)*(x-3) = 0

144*x-24*x^2-21*x-216+63 = 0

123*x-24*x^2-153 = 0

123*x-24*x^2-153 = 0

3*(41*x-8*x^2-51) = 0

41*x-8*x^2-51 = 0

DELTA = 41^2-(-51*(-8)*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-41)/(-8*2) or x = (-49^(1/2)-41)/(-8*2)

x = 17/8 or x = 3

3*(x-17/8)*(x-3) = 0

(3*(x-17/8)*(x-3))/(7*(3*x-9)*(x-3)) = 0

(3*(x-17/8)*(x-3))/(7*(3*x-9)*(x-3)) = 0 // * 7*(3*x-9)*(x-3)

3*(x-17/8)*(x-3) = 0

( x-17/8 )

x-17/8 = 0 // + 17/8

x = 17/8

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x = 17/8

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