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

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Solution for 1/(4x+1)+1(3x-1)=4 equation:


D( x )

4*x+1 = 0

4*x+1 = 0

4*x+1 = 0

4*x+1 = 0 // - 1

4*x = -1 // : 4

x = -1/4

x in (-oo:-1/4) U (-1/4:+oo)

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

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

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

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

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

12*x^2+3*x-16*x-4*x-4-1+1 = 0

12*x^2-13*x-4*x-3-1 = 0

12*x^2-17*x-4 = 0

12*x^2-17*x-4 = 0

12*x^2-17*x-4 = 0

DELTA = (-17)^2-(-4*4*12)

DELTA = 481

DELTA > 0

x = (481^(1/2)+17)/(2*12) or x = (17-481^(1/2))/(2*12)

x = (481^(1/2)+17)/24 or x = (17-481^(1/2))/24

(x-((17-481^(1/2))/24))*(x-((481^(1/2)+17)/24)) = 0

((x-((17-481^(1/2))/24))*(x-((481^(1/2)+17)/24)))/(4*x+1) = 0

((x-((17-481^(1/2))/24))*(x-((481^(1/2)+17)/24)))/(4*x+1) = 0 // * 4*x+1

(x-((17-481^(1/2))/24))*(x-((481^(1/2)+17)/24)) = 0

( x-((17-481^(1/2))/24) )

x-((17-481^(1/2))/24) = 0 // + (17-481^(1/2))/24

x = (17-481^(1/2))/24

( x-((481^(1/2)+17)/24) )

x-((481^(1/2)+17)/24) = 0 // + (481^(1/2)+17)/24

x = (481^(1/2)+17)/24

x in { (17-481^(1/2))/24, (481^(1/2)+17)/24 }

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