(8/(3k-9))-(5/(k-2))=4

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Solution for (8/(3k-9))-(5/(k-2))=4 equation: 


D( k )

k-2 = 0

3*k-9 = 0

k-2 = 0

k-2 = 0

k-2 = 0 // + 2

k = 2

3*k-9 = 0

3*k-9 = 0

3*k-9 = 0 // + 9

3*k = 9 // : 3

k = 9/3

k = 3

k in (-oo:2) U (2:3) U (3:+oo)

8/(3*k-9)-(5/(k-2)) = 4 // - 4

8/(3*k-9)-(5/(k-2))-4 = 0

8/(3*k-9)-5*(k-2)^-1-4 = 0

8/(3*k-9)-5/(k-2)-4 = 0

(8*(k-2))/((3*k-9)*(k-2))+(-5*(3*k-9))/((3*k-9)*(k-2))+(-4*(3*k-9)*(k-2))/((3*k-9)*(k-2)) = 0

8*(k-2)-5*(3*k-9)-4*(3*k-9)*(k-2) = 0

60*k-12*k^2-7*k-72+29 = 0

53*k-12*k^2-43 = 0

53*k-12*k^2-43 = 0

53*k-12*k^2-43 = 0

DELTA = 53^2-(-43*(-12)*4)

DELTA = 745

DELTA > 0

k = (745^(1/2)-53)/(-12*2) or k = (-745^(1/2)-53)/(-12*2)

k = (745^(1/2)-53)/(-24) or k = (745^(1/2)+53)/24

(k-((745^(1/2)-53)/(-24)))*(k-((745^(1/2)+53)/24)) = 0

((k-((745^(1/2)-53)/(-24)))*(k-((745^(1/2)+53)/24)))/((3*k-9)*(k-2)) = 0

((k-((745^(1/2)-53)/(-24)))*(k-((745^(1/2)+53)/24)))/((3*k-9)*(k-2)) = 0 // * (3*k-9)*(k-2)

(k-((745^(1/2)-53)/(-24)))*(k-((745^(1/2)+53)/24)) = 0

( k-((745^(1/2)+53)/24) )

k-((745^(1/2)+53)/24) = 0 // + (745^(1/2)+53)/24

k = (745^(1/2)+53)/24

( k-((745^(1/2)-53)/(-24)) )

k-((745^(1/2)-53)/(-24)) = 0 // + (745^(1/2)-53)/(-24)

k = (745^(1/2)-53)/(-24)

k in { (745^(1/2)+53)/24, (745^(1/2)-53)/(-24) }

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