(4x-8)/abs(x-2)=x

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Solution for (4x-8)/abs(x-2)=x equation: 


D( x )

abs(x-2) = 0

abs(x-2) = 0

abs(x-2) = 0

abs(x-2) = 0

x in (-oo:+oo)

abs(x-2)

x-2 >= 0

x-2 >= 0 // + 2

x >= 2

x in <2:+oo)

x-2 = 0

x in (-oo:2)

-(x-2) = 0

abs(x-2) = 0


/
| -(x-2) = 0 i x in (-oo:2)
| x-2 = 0 i x in <2:+oo)


x in (-oo:2)

-(x-2) = 0

2-x = 0 // - 2

-x = -2 // * -1

x = 2

(-oo:2)

x in <2:+oo)

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:+oo)

(4*x-8)/abs(x-2) = x // - x

(4*x-8)/abs(x-2)-x = 0

(4*x-8)/abs(x-2)-x = 0

x in (-oo:+oo)

abs(x-2)

x-2 >= 0

x-2 >= 0 // + 2

x >= 2

x in <2:+oo)

(4*x-8)/(x-2)-x = 0

x in (-oo:2)

(4*x-8)/(-(x-2))-x = 0

(4*x-8)/abs(x-2)-x = 0


/
| (4*x-8)/(-(x-2))-x = 0 i x in (-oo:2)
| (4*x-8)/(x-2)-x = 0 i x in <2:+oo)


x in (-oo:2)

(4*x-8)/(-(x-2))-x = 0

(4*x-8)/(2-x)-x = 0

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

4*x-x*(2-x)-8 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

x^2+2*x-8 = 0

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

DELTA = 36

DELTA > 0

x = (36^(1/2)-2)/(1*2) or x = (-36^(1/2)-2)/(1*2)

x = 2 or x = -4

(x+4)*(x-2) = 0

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

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

(x+4)*(x-2) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-2 )

x-2 = 0 // + 2

x = 2

x in <2:+oo)

(4*x-8)/(x-2)-x = 0

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

4*x-x*(x-2)-8 = 0

6*x-x^2-8 = 0

6*x-x^2-8 = 0

6*x-x^2-8 = 0

DELTA = 6^2-(-8*(-1)*4)

DELTA = 4

DELTA > 0

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

x = 2 or x = 4

(x-2)*(x-4) = 0

((x-2)*(x-4))/(x-2) = 0

((x-2)*(x-4))/(x-2) = 0 // * x-2

(x-2)*(x-4) = 0

( x-2 )

x-2 = 0 // + 2

x = 2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 2} 

x in { -4, 4 }

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