1/(3x+5)+1/(4x-1)=2

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Solution for 1/(3x+5)+1/(4x-1)=2 equation:


D( x )

3*x+5 = 0

4*x-1 = 0

3*x+5 = 0

3*x+5 = 0

3*x+5 = 0 // - 5

3*x = -5 // : 3

x = -5/3

4*x-1 = 0

4*x-1 = 0

4*x-1 = 0 // + 1

4*x = 1 // : 4

x = 1/4

x in (-oo:-5/3) U (-5/3:1/4) U (1/4:+oo)

1/(3*x+5)+1/(4*x-1) = 2 // - 2

1/(3*x+5)+1/(4*x-1)-2 = 0

(1*(4*x-1))/((3*x+5)*(4*x-1))+(1*(3*x+5))/((3*x+5)*(4*x-1))+(-2*(3*x+5)*(4*x-1))/((3*x+5)*(4*x-1)) = 0

1*(4*x-1)+1*(3*x+5)-2*(3*x+5)*(4*x-1) = 0

7*x-24*x^2-34*x+4+10 = 0

14-24*x^2-27*x = 0

14-24*x^2-27*x = 0

14-24*x^2-27*x = 0

DELTA = (-27)^2-(-24*4*14)

DELTA = 2073

DELTA > 0

x = (2073^(1/2)+27)/(-24*2) or x = (27-2073^(1/2))/(-24*2)

x = (2073^(1/2)+27)/(-48) or x = (27-2073^(1/2))/(-48)

(x-((2073^(1/2)+27)/(-48)))*(x-((27-2073^(1/2))/(-48))) = 0

((x-((2073^(1/2)+27)/(-48)))*(x-((27-2073^(1/2))/(-48))))/((3*x+5)*(4*x-1)) = 0

((x-((2073^(1/2)+27)/(-48)))*(x-((27-2073^(1/2))/(-48))))/((3*x+5)*(4*x-1)) = 0 // * (3*x+5)*(4*x-1)

(x-((2073^(1/2)+27)/(-48)))*(x-((27-2073^(1/2))/(-48))) = 0

( x-((2073^(1/2)+27)/(-48)) )

x-((2073^(1/2)+27)/(-48)) = 0 // + (2073^(1/2)+27)/(-48)

x = (2073^(1/2)+27)/(-48)

( x-((27-2073^(1/2))/(-48)) )

x-((27-2073^(1/2))/(-48)) = 0 // + (27-2073^(1/2))/(-48)

x = (27-2073^(1/2))/(-48)

x in { (2073^(1/2)+27)/(-48), (27-2073^(1/2))/(-48) }

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