3/(x+5)+4/(x-4)=36/(x+5*x-4)

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Solution for 3/(x+5)+4/(x-4)=36/(x+5*x-4) equation: 


D( x )

x+5 = 0

x-4 = 0

x+5*x-4 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x+5*x-4 = 0

x+5*x-4 = 0

6*x-4 = 0 // + 4

6*x = 4 // : 6

x = 4/6

x = 2/3

x in (-oo:-5) U (-5:2/3) U (2/3:4) U (4:+oo)

3/(x+5)+4/(x-4) = 36/(x+5*x-4) // - 36/(x+5*x-4)

3/(x+5)+4/(x-4)-(36/(x+5*x-4)) = 0

3/(x+5)+4/(x-4)-36*(x+5*x-4)^-1 = 0

3/(x+5)+4/(x-4)-36/(6*x-4) = 0

(3*(x-4)*(6*x-4))/((x+5)*(x-4)*(6*x-4))+(4*(x+5)*(6*x-4))/((x+5)*(x-4)*(6*x-4))+(-36*(x+5)*(x-4))/((x+5)*(x-4)*(6*x-4)) = 0

3*(x-4)*(6*x-4)+4*(x+5)*(6*x-4)-36*(x+5)*(x-4) = 0

42*x^2-36*x^2+20*x-36*x-32+720 = 0

6*x^2-16*x+688 = 0

6*x^2-16*x+688 = 0

2*(3*x^2-8*x+344) = 0

3*x^2-8*x+344 = 0

DELTA = (-8)^2-(3*4*344)

DELTA = -4064

DELTA < 0

2 = 0

2/((x+5)*(x-4)*(6*x-4)) = 0

2/((x+5)*(x-4)*(6*x-4)) = 0 // * (x+5)*(x-4)*(6*x-4)

2 = 0

x belongs to the empty set

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