4/(x-2)=1+6/(x+2)

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Solution for 4/(x-2)=1+6/(x+2) equation: 


D( x )

x+2 = 0

x-2 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

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

4/(x-2) = 6/(x+2)+1 // - 6/(x+2)+1

4/(x-2)-(6/(x+2))-1 = 0

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

4/(x-2)-6/(x+2)-1 = 0

(4*(x+2))/((x-2)*(x+2))+(-6*(x-2))/((x-2)*(x+2))+(-1*(x-2)*(x+2))/((x-2)*(x+2)) = 0

4*(x+2)-6*(x-2)-1*(x-2)*(x+2) = 0

4-x^2-2*x+20 = 0

24-x^2-2*x = 0

24-x^2-2*x = 0

24-x^2-2*x = 0

DELTA = (-2)^2-(-1*4*24)

DELTA = 100

DELTA > 0

x = (100^(1/2)+2)/(-1*2) or x = (2-100^(1/2))/(-1*2)

x = -6 or x = 4

(x+6)*(x-4) = 0

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

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

(x+6)*(x-4) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -6, 4 }

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