(7x+6)/(x-6)=(6x-5)/(x-5)

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Solution for (7x+6)/(x-6)=(6x-5)/(x-5) equation: 


D( x )

x-5 = 0

x-6 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x in (-oo:5) U (5:6) U (6:+oo)

(7*x+6)/(x-6) = (6*x-5)/(x-5) // - (6*x-5)/(x-5)

(7*x+6)/(x-6)-((6*x-5)/(x-5)) = 0

(7*x+6)/(x-6)+(-1*(6*x-5))/(x-5) = 0

((7*x+6)*(x-5))/((x-6)*(x-5))+(-1*(6*x-5)*(x-6))/((x-6)*(x-5)) = 0

(7*x+6)*(x-5)-1*(6*x-5)*(x-6) = 0

x^2+12*x-60 = 0

x^2+12*x-60 = 0

x^2+12*x-60 = 0

DELTA = 12^2-(-60*1*4)

DELTA = 384

DELTA > 0

x = (384^(1/2)-12)/(1*2) or x = (-384^(1/2)-12)/(1*2)

x = (8*6^(1/2)-12)/2 or x = (-8*6^(1/2)-12)/2

(x-((-8*6^(1/2)-12)/2))*(x-((8*6^(1/2)-12)/2)) = 0

((x-((-8*6^(1/2)-12)/2))*(x-((8*6^(1/2)-12)/2)))/((x-6)*(x-5)) = 0

((x-((-8*6^(1/2)-12)/2))*(x-((8*6^(1/2)-12)/2)))/((x-6)*(x-5)) = 0 // * (x-6)*(x-5)

(x-((-8*6^(1/2)-12)/2))*(x-((8*6^(1/2)-12)/2)) = 0

( x-((-8*6^(1/2)-12)/2) )

x-((-8*6^(1/2)-12)/2) = 0 // + (-8*6^(1/2)-12)/2

x = (-8*6^(1/2)-12)/2

( x-((8*6^(1/2)-12)/2) )

x-((8*6^(1/2)-12)/2) = 0 // + (8*6^(1/2)-12)/2

x = (8*6^(1/2)-12)/2

x in { (-8*6^(1/2)-12)/2, (8*6^(1/2)-12)/2 }

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