(3)/(x-3)-(x)/(x-4)=(-5)/(x^2-7x+12)

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Solution for (3)/(x-3)-(x)/(x-4)=(-5)/(x^2-7x+12) equation: 


D( x )

x-3 = 0

x-4 = 0

x^2-(7*x)+12 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x^2-(7*x)+12 = 0

x^2-(7*x)+12 = 0

x^2-7*x+12 = 0

x^2-7*x+12 = 0

DELTA = (-7)^2-(1*4*12)

DELTA = 1

DELTA > 0

x = (1^(1/2)+7)/(1*2) or x = (7-1^(1/2))/(1*2)

x = 4 or x = 3

x in (-oo:3) U (3:4) U (4:+oo)

3/(x-3)-(x/(x-4)) = -5/(x^2-(7*x)+12) // + -5/(x^2-(7*x)+12)

3/(x-3)-(x/(x-4))-(-5/(x^2-(7*x)+12)) = 0

3/(x-3)-(x/(x-4))+5*(x^2-7*x+12)^-1 = 0

3/(x-3)+(-1*x)/(x-4)+5/(x^2-7*x+12) = 0

x^2-7*x+12 = 0

x^2-7*x+12 = 0

x^2-7*x+12 = 0

DELTA = (-7)^2-(1*4*12)

DELTA = 1

DELTA > 0

x = (1^(1/2)+7)/(1*2) or x = (7-1^(1/2))/(1*2)

x = 4 or x = 3

(x-3)*(x-4) = 0

3/(x-3)+(-1*x)/(x-4)+5/((x-3)*(x-4)) = 0

(3*(x-4))/((x-3)*(x-4))+(-1*x*(x-3))/((x-3)*(x-4))+5/((x-3)*(x-4)) = 0

3*(x-4)-1*x*(x-3)+5 = 0

6*x-x^2-12+5 = 0

6*x-x^2-7 = 0

6*x-x^2-7 = 0

6*x-x^2-7 = 0

DELTA = 6^2-(-7*(-1)*4)

DELTA = 8

DELTA > 0

x = (8^(1/2)-6)/(-1*2) or x = (-8^(1/2)-6)/(-1*2)

x = (2*2^(1/2)-6)/(-2) or x = (-2*2^(1/2)-6)/(-2)

(x-((2*2^(1/2)-6)/(-2)))*(x-((-2*2^(1/2)-6)/(-2))) = 0

((x-((2*2^(1/2)-6)/(-2)))*(x-((-2*2^(1/2)-6)/(-2))))/((x-3)*(x-4)) = 0

((x-((2*2^(1/2)-6)/(-2)))*(x-((-2*2^(1/2)-6)/(-2))))/((x-3)*(x-4)) = 0 // * (x-3)*(x-4)

(x-((2*2^(1/2)-6)/(-2)))*(x-((-2*2^(1/2)-6)/(-2))) = 0

( x-((-2*2^(1/2)-6)/(-2)) )

x-((-2*2^(1/2)-6)/(-2)) = 0 // + (-2*2^(1/2)-6)/(-2)

x = (-2*2^(1/2)-6)/(-2)

( x-((2*2^(1/2)-6)/(-2)) )

x-((2*2^(1/2)-6)/(-2)) = 0 // + (2*2^(1/2)-6)/(-2)

x = (2*2^(1/2)-6)/(-2)

x in { (-2*2^(1/2)-6)/(-2), (2*2^(1/2)-6)/(-2) }

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