2/(x+5)-3/(x-5)=4x/(x^2-25)

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Solution for 2/(x+5)-3/(x-5)=4x/(x^2-25) equation:


D( x )

x-5 = 0

x+5 = 0

x^2-25 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

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+5)-(3/(x-5)) = (4*x)/(x^2-25) // - (4*x)/(x^2-25)

2/(x+5)-(3/(x-5))-((4*x)/(x^2-25)) = 0

2/(x+5)-3*(x-5)^-1-4*x*(x^2-25)^-1 = 0

2/(x+5)-3/(x-5)+(-4*x)/(x^2-25) = 0

(2*(x-5)*(x^2-25))/((x+5)*(x-5)*(x^2-25))+(-3*(x+5)*(x^2-25))/((x+5)*(x-5)*(x^2-25))+(-4*x*(x+5)*(x-5))/((x+5)*(x-5)*(x^2-25)) = 0

2*(x-5)*(x^2-25)-3*(x+5)*(x^2-25)-4*x*(x+5)*(x-5) = 0

25*x-x^3-4*x^3-25*x^2+100*x+625 = 0

125*x-5*x^3-25*x^2+625 = 0

125*x-5*x^3-25*x^2+625 = 0

5*(25*x-x^3-5*x^2+125) = 0

25*x-x^3-5*x^2+125

5*(25-x^2)-x^3+25*x

x*(25-x^2)+5*(25-x^2)

(x+5)*(25-x^2)

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

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

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

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

( 25-x^2 )

-1*x^2 = -25 // : -1

x^2 = 25

x^2 = 25 // ^ 1/2

abs(x) = 5

x = 5 or x = -5

( x+5 )

x+5 = 0 // - 5

x = -5

x in { 5}

x in { -5}

x belongs to the empty set

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