4/(x^2-x-2)=(x+32)/(x^2-x-2)-28/(x^2-2x-3)

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Solution for 4/(x^2-x-2)=(x+32)/(x^2-x-2)-28/(x^2-2x-3) equation: 


D( x )

x^2-x-2 = 0

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

x^2-x-2 = 0

x^2-x-2 = 0

x^2-x-2 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)+1)/(1*2) or x = (1-9^(1/2))/(1*2)

x = 2 or x = -1

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

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

x^2-2*x-3 = 0

x^2-2*x-3 = 0

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

DELTA = 16

DELTA > 0

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

x = 3 or x = -1

x in (-oo:-1) U (-1:2) U (2:3) U (3:+oo)

4/(x^2-x-2) = (x+32)/(x^2-x-2)-(28/(x^2-(2*x)-3)) // - (x+32)/(x^2-x-2)-(28/(x^2-(2*x)-3))

4/(x^2-x-2)-((x+32)/(x^2-x-2))+28/(x^2-(2*x)-3) = 0

4/(x^2-x-2)-((x+32)/(x^2-x-2))+28/(x^2-2*x-3) = 0

4/(x^2-x-2)+(-1*(x+32))/(x^2-x-2)+28/(x^2-2*x-3) = 0

x^2-x-2 = 0

x^2-x-2 = 0

x^2-x-2 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)+1)/(1*2) or x = (1-9^(1/2))/(1*2)

x = 2 or x = -1

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

x^2-2*x-3 = 0

x^2-2*x-3 = 0

x^2-2*x-3 = 0

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

DELTA = 16

DELTA > 0

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

x = 3 or x = -1

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

4/((x+1)*(x-2))+(-1*(x+32))/((x+1)*(x-2))+28/((x+1)*(x-3)) = 0

4/((x+1)*(x-2))+(-1*(x+32))/((x+1)*(x-2))+(28*(x-2))/((x+1)*(x-2)) = 0

28*(x-2)-1*(x+32)+4 = 0

28*x-x-56-28 = 0

27*x-84 = 0

(27*x-84)/((x+1)*(x-2)) = 0

(27*x-84)/((x+1)*(x-2)) = 0 // * (x+1)*(x-2)

27*x-84 = 0

27*x-84 = 0 // + 84

27*x = 84 // : 27

x = 84/27

x = 28/9

x = 28/9

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