(5n-15)/(4n^2-16n+16)=(1)/(4n-8)+(3)/(2n-4)

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Solution for (5n-15)/(4n^2-16n+16)=(1)/(4n-8)+(3)/(2n-4) equation: 


D( n )

4*n^2-(16*n)+16 = 0

4*n-8 = 0

2*n-4 = 0

4*n^2-(16*n)+16 = 0

4*n^2-(16*n)+16 = 0

4*n^2-16*n+16 = 0

4*n^2-16*n+16 = 0

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

DELTA = 0

n = 16/(2*4)

n = 2 or n = 2

4*n-8 = 0

4*n-8 = 0

4*n-8 = 0 // + 8

4*n = 8 // : 4

n = 8/4

n = 2

2*n-4 = 0

2*n-4 = 0

2*n-4 = 0 // + 4

2*n = 4 // : 2

n = 4/2

n = 2

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

(5*n-15)/(4*n^2-(16*n)+16) = 1/(4*n-8)+3/(2*n-4) // - 1/(4*n-8)+3/(2*n-4)

(5*n-15)/(4*n^2-(16*n)+16)-(1/(4*n-8))-(3/(2*n-4)) = 0

(5*n-15)/(4*n^2-16*n+16)-(4*n-8)^-1-3*(2*n-4)^-1 = 0

(5*n-15)/(4*n^2-16*n+16)-1/(4*n-8)-3/(2*n-4) = 0

4*n^2-16*n+16 = 0

4*n^2-16*n+16 = 0

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

n^2-4*n+4 = 0

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

DELTA = 0

n = 4/(1*2)

n = 2 or n = 2

4*(n-2)^2 = 0

(5*n-15)/(4*(n-2)^2)-1/(4*n-8)-3/(2*n-4) = 0

((5*n-15)*(4*n-8)*(2*n-4))/(4*(n-2)^2*(4*n-8)*(2*n-4))+(-1*4*(n-2)^2*(2*n-4))/(4*(n-2)^2*(4*n-8)*(2*n-4))+(-3*4*(n-2)^2*(4*n-8))/(4*(n-2)^2*(4*n-8)*(2*n-4)) = 0

(5*n-15)*(4*n-8)*(2*n-4)-1*4*(n-2)^2*(2*n-4)-3*4*(n-2)^2*(4*n-8) = 0

32*n^3-48*n^3-232*n^2+288*n^2+544*n-576*n-416+384 = 0

56*n^2-16*n^3-32*n-32 = 0

56*n^2-16*n^3-32*n-32 = 0

8*(7*n^2-2*n^3-4*n-4) = 0

7*n^2-2*n^3-4*n-4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

n = 1

7*n^2-2*n^3-4*n-4 = -3

1

-1

n = -1

7*n^2-2*n^3-4*n-4 = 9

-1

2

n = 2

7*n^2-2*n^3-4*n-4 = 0

2

n-2

3*n-2*n^2+2

7*n^2-2*n^3-4*n-4

n-2

2*n^3-4*n^2

3*n^2-4*n-4

6*n-3*n^2

2*n-4

4-2*n

0

3*n-2*n^2+2 = 0

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

DELTA = 25

DELTA > 0

n = (25^(1/2)-3)/(-2*2) or n = (-25^(1/2)-3)/(-2*2)

n = -1/2 or n = 2

n in { -1/2, 2, 2} 

8*(n+1/2)*(n-2)^2 = 0

(8*(n+1/2)*(n-2)^2)/(4*(n-2)^2*(4*n-8)*(2*n-4)) = 0

(8*(n+1/2)*(n-2)^2)/(4*(n-2)^2*(4*n-8)*(2*n-4)) = 0 // * 4*(n-2)^2*(4*n-8)*(2*n-4)

8*(n+1/2)*(n-2)^2 = 0

( n+1/2 )

n+1/2 = 0 // - 1/2

n = -1/2

( n-2 )

n-2 = 0 // + 2

n = 2

n in { 2} 

n = -1/2

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