(8k/(k-3))+1=((6k-2)/(k^2-4k+3))

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Solution for (8k/(k-3))+1=((6k-2)/(k^2-4k+3)) equation:


D( k )

k-3 = 0

k^2-(4*k)+3 = 0

k-3 = 0

k-3 = 0

k-3 = 0 // + 3

k = 3

k^2-(4*k)+3 = 0

k^2-(4*k)+3 = 0

k^2-4*k+3 = 0

k^2-4*k+3 = 0

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

DELTA = 4

DELTA > 0

k = (4^(1/2)+4)/(1*2) or k = (4-4^(1/2))/(1*2)

k = 3 or k = 1

k in (-oo:1) U (1:3) U (3:+oo)

(8*k)/(k-3)+1 = (6*k-2)/(k^2-(4*k)+3) // - (6*k-2)/(k^2-(4*k)+3)

(8*k)/(k-3)-((6*k-2)/(k^2-(4*k)+3))+1 = 0

(8*k)/(k-3)-((6*k-2)/(k^2-4*k+3))+1 = 0

(8*k)/(k-3)+(-1*(6*k-2))/(k^2-4*k+3)+1 = 0

k^2-4*k+3 = 0

k^2-4*k+3 = 0

k^2-4*k+3 = 0

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

DELTA = 4

DELTA > 0

k = (4^(1/2)+4)/(1*2) or k = (4-4^(1/2))/(1*2)

k = 3 or k = 1

(k-1)*(k-3) = 0

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

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

8*k*(k-1)-1*(6*k-2)+1*(k-3)*(k-1) = 0

8*k^2+k^2-14*k-4*k+2+3 = 0

9*k^2-18*k+5 = 0

9*k^2-18*k+5 = 0

9*k^2-18*k+5 = 0

DELTA = (-18)^2-(4*5*9)

DELTA = 144

DELTA > 0

k = (144^(1/2)+18)/(2*9) or k = (18-144^(1/2))/(2*9)

k = 5/3 or k = 1/3

(k-1/3)*(k-5/3) = 0

((k-1/3)*(k-5/3))/((k-3)*(k-1)) = 0

((k-1/3)*(k-5/3))/((k-3)*(k-1)) = 0 // * (k-3)*(k-1)

(k-1/3)*(k-5/3) = 0

( k-1/3 )

k-1/3 = 0 // + 1/3

k = 1/3

( k-5/3 )

k-5/3 = 0 // + 5/3

k = 5/3

k in { 1/3, 5/3 }

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