(2x/(x^2-5x))-(10/(x^2-25))

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Solution for (2x/(x^2-5x))-(10/(x^2-25)) equation:


D( x )

x^2-25 = 0

x^2-(5*x) = 0

x^2-25 = 0

x^2-25 = 0

1*x^2 = 25 // : 1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x^2-(5*x) = 0

x^2-(5*x) = 0

x^2-5*x = 0

x^2-5*x = 0

DELTA = (-5)^2-(0*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+5)/(1*2) or x = (5-25^(1/2))/(1*2)

x = 5 or x = 0

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

(2*x)/(x^2-(5*x))-(10/(x^2-25)) = 0

(2*x)/(x^2-5*x)-10*(x^2-25)^-1 = 0

(2*x)/(x^2-5*x)-10/(x^2-25) = 0

x^2-5*x = 0

x^2-5*x = 0

x*(x-5) = 0

x-5 = 0 // + 5

x = 5

x*(x-5) = 0

(2*x)/(x*(x-5))-10/(x^2-25) = 0

(2*x*(x^2-25))/(x*(x-5)*(x^2-25))+(-10*x*(x-5))/(x*(x-5)*(x^2-25)) = 0

2*x*(x^2-25)-10*x*(x-5) = 0

2*x^3-10*x^2 = 0

2*x^3-10*x^2 = 0

2*x^2*(x-5) = 0

x-5 = 0 // + 5

x = 5

2*x^2*(x-5) = 0

(2*x^2*(x-5))/(x*(x-5)*(x^2-25)) = 0

(2*x^2*(x-5))/(x*(x-5)*(x^2-25)) = 0 // * x*(x-5)*(x^2-25)

2*x^2*(x-5) = 0

( 2*x^2 )

2*x^2 = 0 // : 2

x^2 = 0

x = 0

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 0}

x in { 5}

x belongs to the empty set

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