1/(2X+1)=1/(-X^2+8X-9)

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Solution for 1/(2X+1)=1/(-X^2+8X-9) equation: 


D( X )

2*X+1 = 0

(-X)^2+8*X-9 = 0

2*X+1 = 0

2*X+1 = 0

2*X+1 = 0 // - 1

2*X = -1 // : 2

X = -1/2

(-X)^2+8*X-9 = 0

(-X)^2+8*X-9 = 0

X^2+8*X-9 = 0

DELTA = 8^2-(-9*1*4)

DELTA = 100

DELTA > 0

X = (100^(1/2)-8)/(1*2) or X = (-100^(1/2)-8)/(1*2)

X = 1 or X = -9

X in (-oo:-9) U (-9:-1/2) U (-1/2:1) U (1:+oo)

1/(2*X+1) = 1/((-X)^2+8*X-9) // - 1/((-X)^2+8*X-9)

1/(2*X+1)-(1/((-X)^2+8*X-9)) = 0

1/(2*X+1)-((-X)^2+8*X-9)^-1 = 0

1/(2*X+1)-1/(X^2+8*X-9) = 0

X^2+8*X-9 = 0

X^2+8*X-9 = 0

X^2+8*X-9 = 0

DELTA = 8^2-(-9*1*4)

DELTA = 100

DELTA > 0

X = (100^(1/2)-8)/(1*2) or X = (-100^(1/2)-8)/(1*2)

X = 1 or X = -9

(X+9)*(X-1) = 0

1/(2*X+1)-1/((X+9)*(X-1)) = 0

(1*(X+9)*(X-1))/((2*X+1)*(X+9)*(X-1))+(-1*(2*X+1))/((2*X+1)*(X+9)*(X-1)) = 0

1*(X+9)*(X-1)-1*(2*X+1) = 0

X^2+6*X-10 = 0

X^2+6*X-10 = 0

X^2+6*X-10 = 0

DELTA = 6^2-(-10*1*4)

DELTA = 76

DELTA > 0

X = (76^(1/2)-6)/(1*2) or X = (-76^(1/2)-6)/(1*2)

X = (2*19^(1/2)-6)/2 or X = (-2*19^(1/2)-6)/2

(X-((-2*19^(1/2)-6)/2))*(X-((2*19^(1/2)-6)/2)) = 0

((X-((-2*19^(1/2)-6)/2))*(X-((2*19^(1/2)-6)/2)))/((2*X+1)*(X+9)*(X-1)) = 0

((X-((-2*19^(1/2)-6)/2))*(X-((2*19^(1/2)-6)/2)))/((2*X+1)*(X+9)*(X-1)) = 0 // * (2*X+1)*(X+9)*(X-1)

(X-((-2*19^(1/2)-6)/2))*(X-((2*19^(1/2)-6)/2)) = 0

( X-((-2*19^(1/2)-6)/2) )

X-((-2*19^(1/2)-6)/2) = 0 // + (-2*19^(1/2)-6)/2

X = (-2*19^(1/2)-6)/2

( X-((2*19^(1/2)-6)/2) )

X-((2*19^(1/2)-6)/2) = 0 // + (2*19^(1/2)-6)/2

X = (2*19^(1/2)-6)/2

X in { (-2*19^(1/2)-6)/2, (2*19^(1/2)-6)/2 }

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