(4X+3)/(3x+2)=(x-8)/(x-6)

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Solution for (4X+3)/(3x+2)=(x-8)/(x-6) equation: 


D( x )

x-6 = 0

3*x+2 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

3*x+2 = 0

3*x+2 = 0

3*x+2 = 0 // - 2

3*x = -2 // : 3

x = -2/3

x in (-oo:-2/3) U (-2/3:6) U (6:+oo)

(4*X+3)/(3*x+2) = (x-8)/(x-6) // - (x-8)/(x-6)

(4*X+3)/(3*x+2)-((x-8)/(x-6)) = 0

(4*X+3)/(3*x+2)+(-1*(x-8))/(x-6) = 0

((4*X+3)*(x-6))/((3*x+2)*(x-6))+(-1*(x-8)*(3*x+2))/((3*x+2)*(x-6)) = 0

(4*X+3)*(x-6)-1*(x-8)*(3*x+2) = 0

4*X*x-24*X-3*x^2+25*x-2 = 0

(4*X*x-24*X-3*x^2+25*x-2)/((3*x+2)*(x-6)) = 0

(4*X*x-24*X-3*x^2+25*x-2)/((3*x+2)*(x-6)) = 0 // * (3*x+2)*(x-6)

4*X*x-24*X-3*x^2+25*x-2 = 0

25*x-24*X-3*x^2-2 = 0

DELTA = 25^2-(-3*4*(-24*X-2))

DELTA = 12*(-24*X-2)+625

12*(-24*X-2)+625 = 0

12*(-24*X-2)+625 = 0

601-288*X = 0

601-288*X = 0

601-288*X = 0 // - 601

-288*X = -601 // : -288

X = -601/(-288)

X = 601/288

DELTA = 0  <=>  t_3 = 601/288

x = -25/(-3*2) i X = 601/288

x = 25/6 i X = 601/288

( x = ((12*(-24*X-2)+625)^(1/2)-25)/(-3*2) or x = (-(12*(-24*X-2)+625)^(1/2)-25)/(-3*2) ) i X > 601/288

( x = ((12*(-24*X-2)+625)^(1/2)-25)/(-6) or x = ((12*(-24*X-2)+625)^(1/2)+25)/6 ) i X > 601/288

X-601/288 > 0

X-601/288 > 0 // + 601/288

X > 601/288

x in { 25/6, ((12*(-24*X-2)+625)^(1/2)-25)/(-6), ((12*(-24*X-2)+625)^(1/2)+25)/6 }

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