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

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


D( x )

3*x+4 = 0

x-1 = 0

3*x+4 = 0

3*x+4 = 0

3*x+4 = 0 // - 4

3*x = -4 // : 3

x = -4/3

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:-4/3) U (-4/3:1) U (1:+oo)

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

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

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

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

9*x-6*x^2-2*x+5+8 = 0

7*x-6*x^2+13 = 0

7*x-6*x^2+13 = 0

7*x-6*x^2+13 = 0

DELTA = 7^2-(-6*4*13)

DELTA = 361

DELTA > 0

x = (361^(1/2)-7)/(-6*2) or x = (-361^(1/2)-7)/(-6*2)

x = -1 or x = 13/6

(x+1)*(x-13/6) = 0

((x+1)*(x-13/6))/((3*x+4)*(x-1)) = 0

((x+1)*(x-13/6))/((3*x+4)*(x-1)) = 0 // * (3*x+4)*(x-1)

(x+1)*(x-13/6) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-13/6 )

x-13/6 = 0 // + 13/6

x = 13/6

x in { -1, 13/6 }

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