x/(2x+2)=(2x-3)/(x-1)-(2x)/(4x+4)

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Solution for x/(2x+2)=(2x-3)/(x-1)-(2x)/(4x+4) equation:


D( x )

2*x+2 = 0

4*x+4 = 0

x-1 = 0

2*x+2 = 0

2*x+2 = 0

2*x+2 = 0 // - 2

2*x = -2 // : 2

x = -2/2

x = -1

4*x+4 = 0

4*x+4 = 0

4*x+4 = 0 // - 4

4*x = -4 // : 4

x = -4/4

x = -1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:-1) U (-1:1) U (1:+oo)

x/(2*x+2) = (2*x-3)/(x-1)-((2*x)/(4*x+4)) // - (2*x-3)/(x-1)-((2*x)/(4*x+4))

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

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

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

x*(x-1)*(4*x+4)-1*(2*x-3)*(2*x+2)*(4*x+4)+2*x*(2*x+2)*(x-1) = 0

4*x^3-12*x^3-8*x^2+28*x-4*x+24 = 0

24*x-8*x^3-8*x^2+24 = 0

24*x-8*x^3-8*x^2+24 = 0

8*(3*x-x^3-x^2+3) = 0

3*x-x^3-x^2+3

3*x-x^2*(x+1)+3

3*(x+1)-x^2*(x+1)

(3-x^2)*(x+1)

8*(3-x^2)*(x+1) = 0

(8*(3-x^2)*(x+1))/((2*x+2)*(x-1)*(4*x+4)) = 0

(8*(3-x^2)*(x+1))/((2*x+2)*(x-1)*(4*x+4)) = 0 // * (2*x+2)*(x-1)*(4*x+4)

8*(3-x^2)*(x+1) = 0

( 3-x^2 )

-1*x^2 = -3 // : -1

x^2 = 3

x^2 = 3 // ^ 1/2

abs(x) = 3^(1/2)

x = 3^(1/2) or x = -3^(1/2)

( x+1 )

x+1 = 0 // - 1

x = -1

x in { -1}

x in { 3^(1/2), -3^(1/2) }

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