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

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


D( x )

2*x+1 = 0

3*x-1 = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

3*x-1 = 0

3*x-1 = 0

3*x-1 = 0 // + 1

3*x = 1 // : 3

x = 1/3

x in (-oo:-1/2) U (-1/2:1/3) U (1/3:+oo)

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

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

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

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

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

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

10*x-30*x^2-5*x-5+5 = 0

5*x-30*x^2 = 0

5*x-30*x^2 = 0

5*x*(1-6*x) = 0

1-6*x = 0 // - 1

-6*x = -1 // : -6

x = -1/(-6)

x = 1/6

5*x*(x-1/6) = 0

(5*x*(x-1/6))/((2*x+1)*(3*x-1)) = 0

(5*x*(x-1/6))/((2*x+1)*(3*x-1)) = 0 // * (2*x+1)*(3*x-1)

5*x*(x-1/6) = 0

( 5*x )

5*x = 0 // : 5

x = 0

( x-1/6 )

x-1/6 = 0 // + 1/6

x = 1/6

x in { 0, 1/6 }

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