(3x+1)/(6x+2)=(2x+5)/(4x-13)

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Solution for (3x+1)/(6x+2)=(2x+5)/(4x-13) equation:


D( x )

4*x-13 = 0

6*x+2 = 0

4*x-13 = 0

4*x-13 = 0

4*x-13 = 0 // + 13

4*x = 13 // : 4

x = 13/4

6*x+2 = 0

6*x+2 = 0

6*x+2 = 0 // - 2

6*x = -2 // : 6

x = -2/6

x = -1/3

x in (-oo:-1/3) U (-1/3:13/4) U (13/4:+oo)

(3*x+1)/(6*x+2) = (2*x+5)/(4*x-13) // - (2*x+5)/(4*x-13)

(3*x+1)/(6*x+2)-((2*x+5)/(4*x-13)) = 0

(3*x+1)/(6*x+2)+(-1*(2*x+5))/(4*x-13) = 0

((3*x+1)*(4*x-13))/((6*x+2)*(4*x-13))+(-1*(2*x+5)*(6*x+2))/((6*x+2)*(4*x-13)) = 0

(3*x+1)*(4*x-13)-1*(2*x+5)*(6*x+2) = 0

-69*x-23 = 0

(-69*x-23)/((6*x+2)*(4*x-13)) = 0

(-69*x-23)/((6*x+2)*(4*x-13)) = 0 // * (6*x+2)*(4*x-13)

-69*x-23 = 0

-69*x-23 = 0 // + 23

-69*x = 23 // : -69

x = 23/(-69)

x = -1/3

x in { -1/3}

x belongs to the empty set

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