3/(x+5)-(x-1)/(2x)=-3/(2x^2+10x)

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Solution for 3/(x+5)-(x-1)/(2x)=-3/(2x^2+10x) equation: 


D( x )

x+5 = 0

2*x^2+10*x = 0

2*x = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

2*x^2+10*x = 0

2*x^2+10*x = 0

2*x^2+10*x = 0

DELTA = 10^2-(0*2*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)-10)/(2*2) or x = (-100^(1/2)-10)/(2*2)

x = 0 or x = -5

2*x = 0

2*x = 0

2*x = 0 // : 2

x = 0

x in (-oo:-5) U (-5:0) U (0:+oo)

3/(x+5)-((x-1)/(2*x)) = -3/(2*x^2+10*x) // + -3/(2*x^2+10*x)

3/(x+5)-((x-1)/(2*x))-(-3/(2*x^2+10*x)) = 0

3/(x+5)-((x-1)/(2*x))+3*(2*x^2+10*x)^-1 = 0

3/(x+5)+(-1*(x-1))/(2*x)+3/(2*x^2+10*x) = 0

2*x^2+10*x = 0

2*x^2+10*x = 0

2*x*(x+5) = 0

x+5 = 0 // - 5

x = -5

2*x*(x+5) = 0

3/(x+5)+(-1*(x-1))/(2*x)+3/(2*x*(x+5)) = 0

(2*3*x)/(2*x*(x+5))+(-1*(x-1)*(x+5))/(2*x*(x+5))+3/(2*x*(x+5)) = 0

2*3*x-1*(x-1)*(x+5)+3 = 0

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

2*x-x^2+8 = 0

2*x-x^2+8 = 0

2*x-x^2+8 = 0

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

DELTA = 36

DELTA > 0

x = (36^(1/2)-2)/(-1*2) or x = (-36^(1/2)-2)/(-1*2)

x = -2 or x = 4

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -2, 4 }

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