x-14/(x-1)=4-(2x)/(x-1)

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Solution for x-14/(x-1)=4-(2x)/(x-1) equation:


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:+oo)

x-(14/(x-1)) = 4-((2*x)/(x-1)) // - 4-((2*x)/(x-1))

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

(2*x)/(x-1)-14*(x-1)^-1+x-4 = 0

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

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

x*(x-1)-4*(x-1)+2*x-14 = 0

x^2+2*x-x-4*x-14+4 = 0

x^2+x-4*x-14+4 = 0

x^2-3*x-10 = 0

x^2-3*x-10 = 0

x^2-3*x-10 = 0

DELTA = (-3)^2-(-10*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)

x = 5 or x = -2

(x+2)*(x-5) = 0

((x+2)*(x-5))/(x-1) = 0

((x+2)*(x-5))/(x-1) = 0 // * x-1

(x+2)*(x-5) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -2, 5 }

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