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

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


D( x )

x+3 = 0

6*x+5 = 0

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

6*x+5 = 0

6*x+5 = 0

6*x+5 = 0 // - 5

6*x = -5 // : 6

x = -5/6

x in (-oo:-3) U (-3:-5/6) U (-5/6:+oo)

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

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

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

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

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

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

x^2-22*x-23 = 0

x^2-22*x-23 = 0

x^2-22*x-23 = 0

DELTA = (-22)^2-(-23*1*4)

DELTA = 576

DELTA > 0

x = (576^(1/2)+22)/(1*2) or x = (22-576^(1/2))/(1*2)

x = 23 or x = -1

(x+1)*(x-23) = 0

((x+1)*(x-23))/((6*x+5)*(x+3)) = 0

((x+1)*(x-23))/((6*x+5)*(x+3)) = 0 // * (6*x+5)*(x+3)

(x+1)*(x-23) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-23 )

x-23 = 0 // + 23

x = 23

x in { -1, 23 }

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