x/(x^2-16)-4/(x^2+5x+4)

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Solution for x/(x^2-16)-4/(x^2+5x+4) equation:


D( x )

x^2-16 = 0

x^2+5*x+4 = 0

x^2-16 = 0

x^2-16 = 0

1*x^2 = 16 // : 1

x^2 = 16

x^2 = 16 // ^ 1/2

abs(x) = 4

x = 4 or x = -4

x^2+5*x+4 = 0

x^2+5*x+4 = 0

x^2+5*x+4 = 0

DELTA = 5^2-(1*4*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-5)/(1*2) or x = (-9^(1/2)-5)/(1*2)

x = -1 or x = -4

x in (-oo:-4) U (-4:-1) U (-1:4) U (4:+oo)

x/(x^2-16)-(4/(x^2+5*x+4)) = 0

x/(x^2-16)-4*(x^2+5*x+4)^-1 = 0

x/(x^2-16)-4/(x^2+5*x+4) = 0

x^2+5*x+4 = 0

x^2+5*x+4 = 0

x^2+5*x+4 = 0

DELTA = 5^2-(1*4*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-5)/(1*2) or x = (-9^(1/2)-5)/(1*2)

x = -1 or x = -4

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

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

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

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

x^3+x^2+4*x+64 = 0

x^3+x^2+4*x+64 = 0

x^3+x^2+4*x+64 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64 }

1

x = 1

x^3+x^2+4*x+64 = 70

1

-1

x = -1

x^3+x^2+4*x+64 = 60

-1

2

x = 2

x^3+x^2+4*x+64 = 84

2

-2

x = -2

x^3+x^2+4*x+64 = 52

-2

4

x = 4

x^3+x^2+4*x+64 = 160

4

-4

x = -4

x^3+x^2+4*x+64 = 0

-4

x+4

x^2-3*x+16

x^3+x^2+4*x+64

x+4

-x^3-4*x^2

4*x-3*x^2+64

3*x^2+12*x

16*x+64

-16*x-64

0

x^2-3*x+16 = 0

DELTA = (-3)^2-(1*4*16)

DELTA = -55

DELTA < 0

x in { -4}

x+4 = 0

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

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

x+4 = 0

x+4 = 0 // - 4

x = -4

x in { -4}

x belongs to the empty set

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