8/(x-4)+(x-68)/(x^2-16)

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Solution for 8/(x-4)+(x-68)/(x^2-16) equation: 


D( x )

x^2-16 = 0

x-4 = 0

x^2-16 = 0

x^2-16 = 0

1*x^2 = 16 // : 1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

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

8/(x-4)+(x-68)/(x^2-16) = 0

(8*(x^2-16))/((x-4)*(x^2-16))+((x-68)*(x-4))/((x-4)*(x^2-16)) = 0

8*(x^2-16)+(x-68)*(x-4) = 0

9*x^2-72*x+144 = 0

9*x^2-72*x+144 = 0

9*(x^2-8*x+16) = 0

x^2-8*x+16 = 0

DELTA = (-8)^2-(1*4*16)

DELTA = 0

x = 8/(1*2)

x = 4 or x = 4

9*(x-4)^2 = 0

(9*(x-4)^2)/((x-4)*(x^2-16)) = 0

(9*(x-4)^2)/((x-4)*(x^2-16)) = 0 // * (x-4)*(x^2-16)

9*(x-4)^2 = 0

x-4 = 0 // + 4

x = 4

x in { 4} 

x belongs to the empty set

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