((x+4)/(x+1))-((3)/(x-3))

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

D( x )

x-3 = 0

x+1 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

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

(x+4)/(x+1)-(3/(x-3)) = 0

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

(x+4)/(x+1)-3/(x-3) = 0

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

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

x^2-2*x-15 = 0

x^2-2*x-15 = 0

x^2-2*x-15 = 0

DELTA = (-2)^2-(-15*1*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)+2)/(1*2) or x = (2-64^(1/2))/(1*2)

x = 5 or x = -3

(x+3)*(x-5) = 0

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

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

(x+3)*(x-5) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -3, 5 }