(3x+4)/(2x+1)=(x-12)/(x-7)

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Solution for (3x+4)/(2x+1)=(x-12)/(x-7) equation:


D( x )

2*x+1 = 0

x-7 = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

x-7 = 0

x-7 = 0

x-7 = 0 // + 7

x = 7

x in (-oo:-1/2) U (-1/2:7) U (7:+oo)

(3*x+4)/(2*x+1) = (x-12)/(x-7) // - (x-12)/(x-7)

(3*x+4)/(2*x+1)-((x-12)/(x-7)) = 0

(3*x+4)/(2*x+1)+(-1*(x-12))/(x-7) = 0

((3*x+4)*(x-7))/((2*x+1)*(x-7))+(-1*(x-12)*(2*x+1))/((2*x+1)*(x-7)) = 0

(3*x+4)*(x-7)-1*(x-12)*(2*x+1) = 0

x^2+6*x-16 = 0

x^2+6*x-16 = 0

x^2+6*x-16 = 0

DELTA = 6^2-(-16*1*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)-6)/(1*2) or x = (-100^(1/2)-6)/(1*2)

x = 2 or x = -8

(x+8)*(x-2) = 0

((x+8)*(x-2))/((2*x+1)*(x-7)) = 0

((x+8)*(x-2))/((2*x+1)*(x-7)) = 0 // * (2*x+1)*(x-7)

(x+8)*(x-2) = 0

( x+8 )

x+8 = 0 // - 8

x = -8

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -8, 2 }

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