((x-6)/(4x-28)-(x-5)/(2x-14))

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Solution for ((x-6)/(4x-28)-(x-5)/(2x-14)) equation:


D( x )

2*x-14 = 0

4*x-28 = 0

2*x-14 = 0

2*x-14 = 0

2*x-14 = 0 // + 14

2*x = 14 // : 2

x = 14/2

x = 7

4*x-28 = 0

4*x-28 = 0

4*x-28 = 0 // + 28

4*x = 28 // : 4

x = 28/4

x = 7

x in (-oo:7) U (7:+oo)

(x-6)/(4*x-28)-((x-5)/(2*x-14)) = 0

(x-6)/(4*x-28)+(-1*(x-5))/(2*x-14) = 0

((x-6)*(2*x-14))/((4*x-28)*(2*x-14))+(-1*(x-5)*(4*x-28))/((4*x-28)*(2*x-14)) = 0

(x-6)*(2*x-14)-1*(x-5)*(4*x-28) = 0

22*x-2*x^2-56 = 0

22*x-2*x^2-56 = 0

2*(11*x-x^2-28) = 0

11*x-x^2-28 = 0

DELTA = 11^2-(-28*(-1)*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-11)/(-1*2) or x = (-9^(1/2)-11)/(-1*2)

x = 4 or x = 7

2*(x-4)*(x-7) = 0

(2*(x-4)*(x-7))/((4*x-28)*(2*x-14)) = 0

(2*(x-4)*(x-7))/((4*x-28)*(2*x-14)) = 0 // * (4*x-28)*(2*x-14)

2*(x-4)*(x-7) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x-7 )

x-7 = 0 // + 7

x = 7

x in { 7}

x = 4

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