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

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


D( x )

4*x+1 = 0

4*x+1 = 0

4*x+1 = 0

4*x+1 = 0 // - 1

4*x = -1 // : 4

x = -1/4

x in (-oo:-1/4) U (-1/4:+oo)

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

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

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

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

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

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

4*x^2+5*x = 0

4*x^2+5*x = 0

x*(4*x+5) = 0

4*x+5 = 0 // - 5

4*x = -5 // : 4

x = -5/4

x*(x+5/4) = 0

(x*(x+5/4))/(2*(4*x+1)) = 0

(x*(x+5/4))/(2*(4*x+1)) = 0 // * 2*(4*x+1)

x*(x+5/4) = 0

( x+5/4 )

x+5/4 = 0 // - 5/4

x = -5/4

( x )

x = 0

x in { -5/4, 0 }

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