((3x)/(x^2-9x+20))-((5)/(2x-8))

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Solution for ((3x)/(x^2-9x+20))-((5)/(2x-8)) equation:


D( x )

2*x-8 = 0

x^2-(9*x)+20 = 0

2*x-8 = 0

2*x-8 = 0

2*x-8 = 0 // + 8

2*x = 8 // : 2

x = 8/2

x = 4

x^2-(9*x)+20 = 0

x^2-(9*x)+20 = 0

x^2-9*x+20 = 0

x^2-9*x+20 = 0

DELTA = (-9)^2-(1*4*20)

DELTA = 1

DELTA > 0

x = (1^(1/2)+9)/(1*2) or x = (9-1^(1/2))/(1*2)

x = 5 or x = 4

x in (-oo:4) U (4:5) U (5:+oo)

(3*x)/(x^2-(9*x)+20)-(5/(2*x-8)) = 0

(3*x)/(x^2-9*x+20)-5*(2*x-8)^-1 = 0

(3*x)/(x^2-9*x+20)-5/(2*x-8) = 0

x^2-9*x+20 = 0

x^2-9*x+20 = 0

x^2-9*x+20 = 0

DELTA = (-9)^2-(1*4*20)

DELTA = 1

DELTA > 0

x = (1^(1/2)+9)/(1*2) or x = (9-1^(1/2))/(1*2)

x = 5 or x = 4

(x-4)*(x-5) = 0

(3*x)/((x-4)*(x-5))-5/(2*x-8) = 0

(3*x*(2*x-8))/((x-4)*(x-5)*(2*x-8))+(-5*(x-4)*(x-5))/((x-4)*(x-5)*(2*x-8)) = 0

3*x*(2*x-8)-5*(x-4)*(x-5) = 0

x^2+21*x-100 = 0

x^2+21*x-100 = 0

x^2+21*x-100 = 0

DELTA = 21^2-(-100*1*4)

DELTA = 841

DELTA > 0

x = (841^(1/2)-21)/(1*2) or x = (-841^(1/2)-21)/(1*2)

x = 4 or x = -25

(x+25)*(x-4) = 0

((x+25)*(x-4))/((x-4)*(x-5)*(2*x-8)) = 0

((x+25)*(x-4))/((x-4)*(x-5)*(2*x-8)) = 0 // * (x-4)*(x-5)*(2*x-8)

(x+25)*(x-4) = 0

( x+25 )

x+25 = 0 // - 25

x = -25

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 4}

x = -25

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