(10-x)/(4x)=(1)/(x-1)

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Solution for (10-x)/(4x)=(1)/(x-1) equation:


D( x )

4*x = 0

x-1 = 0

4*x = 0

4*x = 0

4*x = 0 // : 4

x = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:0) U (0:1) U (1:+oo)

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

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

(10-x)/(4*x)-(x-1)^-1 = 0

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

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

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

7*x-x^2-10 = 0

7*x-x^2-10 = 0

7*x-x^2-10 = 0

DELTA = 7^2-(-10*(-1)*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-7)/(-1*2) or x = (-9^(1/2)-7)/(-1*2)

x = 2 or x = 5

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

((x-2)*(x-5))/(4*x*(x-1)) = 0

((x-2)*(x-5))/(4*x*(x-1)) = 0 // * 4*x*(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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