(x/(4*x-16))-8=(1/(x-4))

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Solution for (x/(4*x-16))-8=(1/(x-4)) equation: 


D( x )

4*x-16 = 0

x-4 = 0

4*x-16 = 0

4*x-16 = 0

4*x-16 = 0 // + 16

4*x = 16 // : 4

x = 16/4

x = 4

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

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

x/(4*x-16)-8 = 1/(x-4) // - 1/(x-4)

x/(4*x-16)-(1/(x-4))-8 = 0

x/(4*x-16)-(x-4)^-1-8 = 0

x/(4*x-16)-1/(x-4)-8 = 0

(x*(x-4))/((4*x-16)*(x-4))+(-1*(4*x-16))/((4*x-16)*(x-4))+(-8*(4*x-16)*(x-4))/((4*x-16)*(x-4)) = 0

x*(x-4)-1*(4*x-16)-8*(4*x-16)*(x-4) = 0

x^2-32*x^2-8*x+256*x-512+16 = 0

248*x-31*x^2-496 = 0

248*x-31*x^2-496 = 0

31*(8*x-x^2-16) = 0

8*x-x^2-16 = 0

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

DELTA = 0

x = -8/(-1*2)

x = 4 or x = 4

31*(x-4)^2 = 0

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

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

31*(x-4)^2 = 0

( 31 )

31 = 0

x belongs to the empty set

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 4} 

x belongs to the empty set

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