(4/x)-3=4/(3+x)

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Solution for (4/x)-3=4/(3+x) equation: 


D( x )

x = 0

x+3 = 0

x = 0

x = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

4/x-3 = 4/(x+3) // - 4/(x+3)

4/x-(4/(x+3))-3 = 0

4/x-4*(x+3)^-1-3 = 0

4/x-4/(x+3)-3 = 0

(-4*x)/(x*(x+3))+(4*(x+3))/(x*(x+3))+(-3*x*(x+3))/(x*(x+3)) = 0

4*(x+3)-3*x*(x+3)-4*x = 0

12-3*x^2-9*x = 0

12-3*x^2-9*x = 0

3*(4-x^2-3*x) = 0

4-x^2-3*x = 0

DELTA = (-3)^2-(-1*4*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+3)/(-1*2) or x = (3-25^(1/2))/(-1*2)

x = -4 or x = 1

3*(x+4)*(x-1) = 0

(3*(x+4)*(x-1))/(x*(x+3)) = 0

(3*(x+4)*(x-1))/(x*(x+3)) = 0 // * x*(x+3)

3*(x+4)*(x-1) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -4, 1 }

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