(x-12)/(3-x)=(x+16)/(x+5)

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Solution for (x-12)/(3-x)=(x+16)/(x+5) equation: 


D( x )

x+5 = 0

3-x = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

3-x = 0

3-x = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

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

(x-12)/(3-x) = (x+16)/(x+5) // - (x+16)/(x+5)

(x-12)/(3-x)-((x+16)/(x+5)) = 0

(x-12)/(3-x)+(-1*(x+16))/(x+5) = 0

((x-12)*(x+5))/((3-x)*(x+5))+(-1*(x+16)*(3-x))/((3-x)*(x+5)) = 0

(x-12)*(x+5)-1*(x+16)*(3-x) = 0

2*x^2+6*x-108 = 0

2*x^2+6*x-108 = 0

2*(x^2+3*x-54) = 0

x^2+3*x-54 = 0

DELTA = 3^2-(-54*1*4)

DELTA = 225

DELTA > 0

x = (225^(1/2)-3)/(1*2) or x = (-225^(1/2)-3)/(1*2)

x = 6 or x = -9

2*(x+9)*(x-6) = 0

(2*(x+9)*(x-6))/((3-x)*(x+5)) = 0

(2*(x+9)*(x-6))/((3-x)*(x+5)) = 0 // * (3-x)*(x+5)

2*(x+9)*(x-6) = 0

( x+9 )

x+9 = 0 // - 9

x = -9

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -9, 6 }

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