1/(x-1)+1/(4x-4)=5/4

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Solution for 1/(x-1)+1/(4x-4)=5/4 equation:


D( x )

4*x-4 = 0

x-1 = 0

4*x-4 = 0

4*x-4 = 0

4*x-4 = 0 // + 4

4*x = 4 // : 4

x = 4/4

x = 1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

1/(x-1)+1/(4*x-4) = 5/4 // - 5/4

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

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

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

1*4*(4*x-4)+1*4*(x-1)-5*(x-1)*(4*x-4) = 0

20*x-20*x^2+40*x-20-20 = 0

60*x-20*x^2-40 = 0

60*x-20*x^2-40 = 0

20*(3*x-x^2-2) = 0

3*x-x^2-2 = 0

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

DELTA = 1

DELTA > 0

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

x = 1 or x = 2

20*(x-1)*(x-2) = 0

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

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

20*(x-1)*(x-2) = 0

( x-1 )

x-1 = 0 // + 1

x = 1

( x-2 )

x-2 = 0 // + 2

x = 2

x in { 1}

x = 2

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