((a^2)/(a-4))+((2a+8)/(4-a))

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Solution for ((a^2)/(a-4))+((2a+8)/(4-a)) equation: 


D( a )

a-4 = 0

4-a = 0

a-4 = 0

a-4 = 0

a-4 = 0 // + 4

a = 4

4-a = 0

4-a = 0

4-a = 0 // - 4

-a = -4 // * -1

a = 4

a in (-oo:4) U (4:+oo)

(a^2)/(a-4)+(2*a+8)/(4-a) = 0

(a^2*(4-a))/((a-4)*(4-a))+((2*a+8)*(a-4))/((a-4)*(4-a)) = 0

a^2*(4-a)+(2*a+8)*(a-4) = 0

6*a^2-a^3-32 = 0

6*a^2-a^3-32 = 0

6*a^2-a^3-32 = 0

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

1

a = 1

6*a^2-a^3-32 = -27

1

-1

a = -1

6*a^2-a^3-32 = -25

-1

2

a = 2

6*a^2-a^3-32 = -16

2

-2

a = -2

6*a^2-a^3-32 = 0

-2

a+2

8*a-a^2-16

6*a^2-a^3-32

a+2

a^3+2*a^2

8*a^2-32

-8*a^2-16*a

-16*a-32

16*a+32

0

8*a-a^2-16 = 0

DELTA = 8^2-(-16*(-1)*4)

DELTA = 0

a = -8/(-1*2)

a = 4 or a = 4

a in { 4, 4, -2} 

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

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

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

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

( a+2 )

a+2 = 0 // - 2

a = -2

( a-4 )

a-4 = 0 // + 4

a = 4

a in { 4} 

a = -2

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