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

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


D( x )

x+5 = 0

x^2-25 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

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

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

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

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

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

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

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

2*x^2+2*x^2-50-50 = 0

4*x^2-100 = 0

(4*x^2-100)/((x^2-25)*(x+5)) = 0

(4*x^2-100)/((x^2-25)*(x+5)) = 0 // * (x^2-25)*(x+5)

4*x^2-100 = 0

4*x^2 = 100 // : 4

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

x in { 5} 

x in { -5} 

x belongs to the empty set

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