3/(x-1)+2/(4x-4)=7/4

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Solution for 3/(x-1)+2/(4x-4)=7/4 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)

3/(x-1)+2/(4*x-4) = 7/4 // - 7/4

3/(x-1)+2/(4*x-4)-(7/4) = 0

3/(x-1)+2/(4*x-4)-7/4 = 0

(3*4*(4*x-4))/(4*(x-1)*(4*x-4))+(2*4*(x-1))/(4*(x-1)*(4*x-4))+(-7*(x-1)*(4*x-4))/(4*(x-1)*(4*x-4)) = 0

3*4*(4*x-4)+2*4*(x-1)-7*(x-1)*(4*x-4) = 0

56*x-28*x^2+56*x-56-28 = 0

112*x-28*x^2-84 = 0

112*x-28*x^2-84 = 0

28*(4*x-x^2-3) = 0

4*x-x^2-3 = 0

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

DELTA = 4

DELTA > 0

x = (4^(1/2)-4)/(-1*2) or x = (-4^(1/2)-4)/(-1*2)

x = 1 or x = 3

28*(x-1)*(x-3) = 0

(28*(x-1)*(x-3))/(4*(x-1)*(4*x-4)) = 0

(28*(x-1)*(x-3))/(4*(x-1)*(4*x-4)) = 0 // * 4*(x-1)*(4*x-4)

28*(x-1)*(x-3) = 0

( x-1 )

x-1 = 0 // + 1

x = 1

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 1} 

x = 3

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