((a+5)/(a-2))-((5a+18)/((a^2)-4))

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Solution for ((a+5)/(a-2))-((5a+18)/((a^2)-4)) equation:


D( a )

a-2 = 0

a^2-4 = 0

a-2 = 0

a-2 = 0

a-2 = 0 // + 2

a = 2

a^2-4 = 0

a^2-4 = 0

1*a^2 = 4 // : 1

a^2 = 4

a^2 = 4 // ^ 1/2

abs(a) = 2

a = 2 or a = -2

a in (-oo:-2) U (-2:2) U (2:+oo)

(a+5)/(a-2)-((5*a+18)/(a^2-4)) = 0

(a+5)/(a-2)+(-1*(5*a+18))/(a^2-4) = 0

((a+5)*(a^2-4))/((a-2)*(a^2-4))+(-1*(5*a+18)*(a-2))/((a-2)*(a^2-4)) = 0

(a+5)*(a^2-4)-1*(5*a+18)*(a-2) = 0

a^3-12*a+16 = 0

a^3-12*a+16 = 0

a^3-12*a+16 = 0

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

1

a = 1

a^3-12*a+16 = 5

1

-1

a = -1

a^3-12*a+16 = 27

-1

2

a = 2

a^3-12*a+16 = 0

2

a-2

a^2+2*a-8

a^3-12*a+16

a-2

2*a^2-a^3

2*a^2-12*a+16

4*a-2*a^2

16-8*a

8*a-16

0

a^2+2*a-8 = 0

DELTA = 2^2-(-8*1*4)

DELTA = 36

DELTA > 0

a = (36^(1/2)-2)/(1*2) or a = (-36^(1/2)-2)/(1*2)

a = 2 or a = -4

a in { -4, 2, 2}

(a+4)*(a-2)^2 = 0

((a+4)*(a-2)^2)/((a-2)*(a^2-4)) = 0

((a+4)*(a-2)^2)/((a-2)*(a^2-4)) = 0 // * (a-2)*(a^2-4)

(a+4)*(a-2)^2 = 0

( a+4 )

a+4 = 0 // - 4

a = -4

( a-2 )

a-2 = 0 // + 2

a = 2

a in { 2}

a = -4

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