(x^2-6)/(2x^2+7x+6)+(-2)/(x+2)=(-4)/(2x+3)

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Solution for (x^2-6)/(2x^2+7x+6)+(-2)/(x+2)=(-4)/(2x+3) equation: 


D( x )

x+2 = 0

2*x+3 = 0

2*x^2+7*x+6 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

2*x+3 = 0

2*x+3 = 0

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

2*x^2+7*x+6 = 0

2*x^2+7*x+6 = 0

2*x^2+7*x+6 = 0

DELTA = 7^2-(2*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)-7)/(2*2) or x = (-1^(1/2)-7)/(2*2)

x = -3/2 or x = -2

x in (-oo:-2) U (-2:-3/2) U (-3/2:+oo)

(x^2-6)/(2*x^2+7*x+6)-2/(x+2) = -4/(2*x+3) // + -4/(2*x+3)

(x^2-6)/(2*x^2+7*x+6)-2/(x+2)-(-4/(2*x+3)) = 0

(x^2-6)/(2*x^2+7*x+6)-2/(x+2)+4*(2*x+3)^-1 = 0

(x^2-6)/(2*x^2+7*x+6)-2/(x+2)+4/(2*x+3) = 0

2*x^2+7*x+6 = 0

2*x^2+7*x+6 = 0

2*x^2+7*x+6 = 0

DELTA = 7^2-(2*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)-7)/(2*2) or x = (-1^(1/2)-7)/(2*2)

x = -3/2 or x = -2

(x+2)*(x+3/2) = 0

(x^2-6)/((x+2)*(x+3/2))-2/(x+2)+4/(2*x+3) = 0

((x^2-6)*(2*x+3))/((x+2)*(x+3/2)*(2*x+3))+(-2*(x+3/2)*(2*x+3))/((x+2)*(x+3/2)*(2*x+3))+(4*(x+2)*(x+3/2))/((x+2)*(x+3/2)*(2*x+3)) = 0

(x^2-6)*(2*x+3)-2*(x+3/2)*(2*x+3)+4*(x+2)*(x+3/2) = 0

2*x^3-x^2+4*x^2-24*x+14*x-27+12 = 0

2*x^3+3*x^2-10*x-15 = 0

2*x^3+3*x^2-10*x-15 = 0

2*x^3+3*x^2-10*x-15

x^2*(2*x+3)-10*x-15

x^2*(2*x+3)-5*(2*x+3)

(x^2-5)*(2*x+3)

((x^2-5)*(2*x+3))/((x+2)*(x+3/2)*(2*x+3)) = 0

((x^2-5)*(2*x+3))/((x+2)*(x+3/2)*(2*x+3)) = 0 // * (x+2)*(x+3/2)*(2*x+3)

(x^2-5)*(2*x+3) = 0

( 2*x+3 )

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

( x^2-5 )

1*x^2 = 5 // : 1

x^2 = 5

x^2 = 5 // ^ 1/2

abs(x) = 5^(1/2)

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

x in { -3/2} 

x in { 5^(1/2), -5^(1/2) }

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