(2-x)/(x+2)=(x+3)/(3-x)+6

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Solution for (2-x)/(x+2)=(x+3)/(3-x)+6 equation: 


D( x )

x+2 = 0

3-x = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

3-x = 0

3-x = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

x in (-oo:-2) U (-2:3) U (3:+oo)

(2-x)/(x+2) = (x+3)/(3-x)+6 // - (x+3)/(3-x)+6

(2-x)/(x+2)-((x+3)/(3-x))-6 = 0

(2-x)/(x+2)+(-1*(x+3))/(3-x)-6 = 0

((2-x)*(3-x))/((x+2)*(3-x))+(-1*(x+3)*(x+2))/((x+2)*(3-x))+(-6*(x+2)*(3-x))/((x+2)*(3-x)) = 0

(2-x)*(3-x)-1*(x+3)*(x+2)-6*(x+2)*(3-x) = 0

6*x^2-10*x-6*x-36 = 0

6*x^2-16*x-36 = 0

6*x^2-16*x-36 = 0

2*(3*x^2-8*x-18) = 0

3*x^2-8*x-18 = 0

DELTA = (-8)^2-(-18*3*4)

DELTA = 280

DELTA > 0

x = (280^(1/2)+8)/(2*3) or x = (8-280^(1/2))/(2*3)

x = (2*70^(1/2)+8)/6 or x = (8-2*70^(1/2))/6

2*(x-((8-2*70^(1/2))/6))*(x-((2*70^(1/2)+8)/6)) = 0

(2*(x-((8-2*70^(1/2))/6))*(x-((2*70^(1/2)+8)/6)))/((x+2)*(3-x)) = 0

(2*(x-((8-2*70^(1/2))/6))*(x-((2*70^(1/2)+8)/6)))/((x+2)*(3-x)) = 0 // * (x+2)*(3-x)

2*(x-((8-2*70^(1/2))/6))*(x-((2*70^(1/2)+8)/6)) = 0

( x-((2*70^(1/2)+8)/6) )

x-((2*70^(1/2)+8)/6) = 0 // + (2*70^(1/2)+8)/6

x = (2*70^(1/2)+8)/6

( x-((8-2*70^(1/2))/6) )

x-((8-2*70^(1/2))/6) = 0 // + (8-2*70^(1/2))/6

x = (8-2*70^(1/2))/6

x in { (2*70^(1/2)+8)/6, (8-2*70^(1/2))/6 }

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