5/(2x+4)+3/(x+2)=2

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Solution for 5/(2x+4)+3/(x+2)=2 equation: 


D( x )

x+2 = 0

2*x+4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

2*x+4 = 0

2*x+4 = 0

2*x+4 = 0 // - 4

2*x = -4 // : 2

x = -4/2

x = -2

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

5/(2*x+4)+3/(x+2) = 2 // - 2

5/(2*x+4)+3/(x+2)-2 = 0

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

5*(x+2)+3*(2*x+4)-2*(2*x+4)*(x+2) = 0

11*x-4*x^2-16*x-16+22 = 0

6-4*x^2-5*x = 0

6-4*x^2-5*x = 0

6-4*x^2-5*x = 0

DELTA = (-5)^2-(-4*4*6)

DELTA = 121

DELTA > 0

x = (121^(1/2)+5)/(-4*2) or x = (5-121^(1/2))/(-4*2)

x = -2 or x = 3/4

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x-3/4 )

x-3/4 = 0 // + 3/4

x = 3/4

x in { -2} 

x = 3/4

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