(6x-7)/(7x+6)=(x-1)/(x+2)

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Solution for (6x-7)/(7x+6)=(x-1)/(x+2) equation: 


D( x )

x+2 = 0

7*x+6 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

7*x+6 = 0

7*x+6 = 0

7*x+6 = 0 // - 6

7*x = -6 // : 7

x = -6/7

x in (-oo:-2) U (-2:-6/7) U (-6/7:+oo)

(6*x-7)/(7*x+6) = (x-1)/(x+2) // - (x-1)/(x+2)

(6*x-7)/(7*x+6)-((x-1)/(x+2)) = 0

(6*x-7)/(7*x+6)+(-1*(x-1))/(x+2) = 0

((6*x-7)*(x+2))/((7*x+6)*(x+2))+(-1*(x-1)*(7*x+6))/((7*x+6)*(x+2)) = 0

(6*x-7)*(x+2)-1*(x-1)*(7*x+6) = 0

6*x-x^2-8 = 0

6*x-x^2-8 = 0

6*x-x^2-8 = 0

DELTA = 6^2-(-8*(-1)*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)-6)/(-1*2) or x = (-4^(1/2)-6)/(-1*2)

x = 2 or x = 4

(x-2)*(x-4) = 0

((x-2)*(x-4))/((7*x+6)*(x+2)) = 0

((x-2)*(x-4))/((7*x+6)*(x+2)) = 0 // * (7*x+6)*(x+2)

(x-2)*(x-4) = 0

( x-2 )

x-2 = 0 // + 2

x = 2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 2, 4 }

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