((5x+5)/(3x-2))-((x-2)/(x-3))=((2x+6)/(x-3))

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Solution for ((5x+5)/(3x-2))-((x-2)/(x-3))=((2x+6)/(x-3)) equation:


D( x )

x-3 = 0

3*x-2 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

3*x-2 = 0

3*x-2 = 0

3*x-2 = 0 // + 2

3*x = 2 // : 3

x = 2/3

x in (-oo:2/3) U (2/3:3) U (3:+oo)

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

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

(5*x+5)/(3*x-2)+(-1*(x-2))/(x-3)+(-1*(2*x+6))/(x-3) = 0

((5*x+5)*(x-3))/((3*x-2)*(x-3))+(-1*(x-2)*(3*x-2))/((3*x-2)*(x-3))+(-1*(2*x+6)*(3*x-2))/((3*x-2)*(x-3)) = 0

(5*x+5)*(x-3)-1*(x-2)*(3*x-2)-1*(2*x+6)*(3*x-2) = 0

2*x^2-6*x^2-2*x-14*x-19+12 = 0

-4*x^2-16*x-7 = 0

-4*x^2-16*x-7 = 0

-1*(4*x^2+16*x+7) = 0

4*x^2+16*x+7 = 0

DELTA = 16^2-(4*4*7)

DELTA = 144

DELTA > 0

x = (144^(1/2)-16)/(2*4) or x = (-144^(1/2)-16)/(2*4)

x = -1/2 or x = -7/2

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

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

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

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

( x+1/2 )

x+1/2 = 0 // - 1/2

x = -1/2

( x+7/2 )

x+7/2 = 0 // - 7/2

x = -7/2

x in { -1/2, -7/2 }

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