(3m)/(((m+5)/(m^2))-(3/(m+5)))

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Solution for (3m)/(((m+5)/(m^2))-(3/(m+5))) equation: 


D( m )

m^2 = 0

m+5 = 0

(m+5)/(m^2)-(3/(m+5)) = 0

m^2 = 0

m^2 = 0

1*m^2 = 0 // : 1

m^2 = 0

m = 0

m+5 = 0

m+5 = 0

m+5 = 0 // - 5

m = -5

(m+5)/(m^2)-(3/(m+5)) = 0

(m+5)/(m^2)-(3/(m+5)) = 0

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

(m+5)/(m^2)-3/(m+5) = 0

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

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

10*m-2*m^2+25 = 0

10*m-2*m^2+25 = 0

10*m-2*m^2+25 = 0

DELTA = 10^2-(-2*4*25)

DELTA = 300

DELTA > 0

m = (300^(1/2)-10)/(-2*2) or m = (-300^(1/2)-10)/(-2*2)

m = (10*3^(1/2)-10)/(-4) or m = (-10*3^(1/2)-10)/(-4)

(m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))) = 0

((m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))))/(m^2*(m+5)) = 0

((m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))))/(m^2*(m+5)) = 0 // * m^2*(m+5)

(m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))) = 0

( m-((-10*3^(1/2)-10)/(-4)) )

m-((-10*3^(1/2)-10)/(-4)) = 0 // + (-10*3^(1/2)-10)/(-4)

m = (-10*3^(1/2)-10)/(-4)

( m-((10*3^(1/2)-10)/(-4)) )

m-((10*3^(1/2)-10)/(-4)) = 0 // + (10*3^(1/2)-10)/(-4)

m = (10*3^(1/2)-10)/(-4)

m in (-oo:-5) U (-5:(10*3^(1/2)-10)/(-4)) U ((10*3^(1/2)-10)/(-4):0) U (0:(-10*3^(1/2)-10)/(-4)) U ((-10*3^(1/2)-10)/(-4):+oo)

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

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

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

(m+5)/(m^2)-3/(m+5) = 0

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

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

10*m-2*m^2+25 = 0

10*m-2*m^2+25 = 0

10*m-2*m^2+25 = 0

DELTA = 10^2-(-2*4*25)

DELTA = 300

DELTA > 0

m = (300^(1/2)-10)/(-2*2) or m = (-300^(1/2)-10)/(-2*2)

m = (10*3^(1/2)-10)/(-4) or m = (-10*3^(1/2)-10)/(-4)

(m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))) = 0

((m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))))/(m^2*(m+5)) = 0

((m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))))/(m^2*(m+5)) = 0 // * m^2*(m+5)

(m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4))) = 0

(3*m)/((m-((10*3^(1/2)-10)/(-4)))*(m-((-10*3^(1/2)-10)/(-4)))) = 0

3*m = 0 // : 3

m = 0

m in { 0} 

m belongs to the empty set

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