8/(x-1)=4x

Solution for 8/(x-1)=4x 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)

8/(x-1) = 4*x // - 4*x

8/(x-1)-(4*x) = 0

8/(x-1)-4*x = 0

8/(x-1)+(-4*x*(x-1))/(x-1) = 0

8-4*x*(x-1) = 0

4*x-4*x^2+8 = 0

4*x-4*x^2+8 = 0

4*(x-x^2+2) = 0

x-x^2+2 = 0

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

DELTA = 9

DELTA > 0

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

x = -1 or x = 2

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

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

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

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

( 4 )

4 = 0

x belongs to the empty set

( x+1 )

x+1 = 0 // - 1

x = -1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -1, 2 }