(x-12)/(3-x)=(x+33)/(x+3)

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Solution for (x-12)/(3-x)=(x+33)/(x+3) equation:


D( x )

3-x = 0

x+3 = 0

3-x = 0

3-x = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:3) U (3:+oo)

(x-12)/(3-x) = (x+33)/(x+3) // - (x+33)/(x+3)

(x-12)/(3-x)-((x+33)/(x+3)) = 0

(x-12)/(3-x)+(-1*(x+33))/(x+3) = 0

((x-12)*(x+3))/((3-x)*(x+3))+(-1*(x+33)*(3-x))/((3-x)*(x+3)) = 0

(x-12)*(x+3)-1*(x+33)*(3-x) = 0

2*x^2+21*x-135 = 0

2*x^2+21*x-135 = 0

2*x^2+21*x-135 = 0

DELTA = 21^2-(-135*2*4)

DELTA = 1521

DELTA > 0

x = (1521^(1/2)-21)/(2*2) or x = (-1521^(1/2)-21)/(2*2)

x = 9/2 or x = -15

(x+15)*(x-9/2) = 0

((x+15)*(x-9/2))/((3-x)*(x+3)) = 0

((x+15)*(x-9/2))/((3-x)*(x+3)) = 0 // * (3-x)*(x+3)

(x+15)*(x-9/2) = 0

( x+15 )

x+15 = 0 // - 15

x = -15

( x-9/2 )

x-9/2 = 0 // + 9/2

x = 9/2

x in { -15, 9/2 }

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