(24)/(2x+6)+(1)/(x-3)=13/2

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Solution for (24)/(2x+6)+(1)/(x-3)=13/2 equation: 


D( x )

x-3 = 0

2*x+6 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

2*x+6 = 0

2*x+6 = 0

2*x+6 = 0 // - 6

2*x = -6 // : 2

x = -6/2

x = -3

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

24/(2*x+6)+1/(x-3) = 13/2 // - 13/2

24/(2*x+6)+1/(x-3)-(13/2) = 0

24/(2*x+6)+1/(x-3)-13/2 = 0

(2*24*(x-3))/(2*(2*x+6)*(x-3))+(1*2*(2*x+6))/(2*(2*x+6)*(x-3))+(-13*(2*x+6)*(x-3))/(2*(2*x+6)*(x-3)) = 0

2*24*(x-3)+1*2*(2*x+6)-13*(2*x+6)*(x-3) = 0

52*x-26*x^2-132+234 = 0

52*x-26*x^2+102 = 0

52*x-26*x^2+102 = 0

2*(26*x-13*x^2+51) = 0

26*x-13*x^2+51 = 0

DELTA = 26^2-(-13*4*51)

DELTA = 3328

DELTA > 0

x = (3328^(1/2)-26)/(-13*2) or x = (-3328^(1/2)-26)/(-13*2)

x = (16*13^(1/2)-26)/(-26) or x = (-16*13^(1/2)-26)/(-26)

2*(x-((16*13^(1/2)-26)/(-26)))*(x-((-16*13^(1/2)-26)/(-26))) = 0

(2*(x-((16*13^(1/2)-26)/(-26)))*(x-((-16*13^(1/2)-26)/(-26))))/(2*(2*x+6)*(x-3)) = 0

(2*(x-((16*13^(1/2)-26)/(-26)))*(x-((-16*13^(1/2)-26)/(-26))))/(2*(2*x+6)*(x-3)) = 0 // * 2*(2*x+6)*(x-3)

2*(x-((16*13^(1/2)-26)/(-26)))*(x-((-16*13^(1/2)-26)/(-26))) = 0

( x-((-16*13^(1/2)-26)/(-26)) )

x-((-16*13^(1/2)-26)/(-26)) = 0 // + (-16*13^(1/2)-26)/(-26)

x = (-16*13^(1/2)-26)/(-26)

( x-((16*13^(1/2)-26)/(-26)) )

x-((16*13^(1/2)-26)/(-26)) = 0 // + (16*13^(1/2)-26)/(-26)

x = (16*13^(1/2)-26)/(-26)

x in { (-16*13^(1/2)-26)/(-26), (16*13^(1/2)-26)/(-26) }

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