2x/(x^2-4)=(8/(x+2))-(7/(x-2))

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Solution for 2x/(x^2-4)=(8/(x+2))-(7/(x-2)) equation: 


D( x )

x-2 = 0

x+2 = 0

x^2-4 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:2) U (2:+oo)

(2*x)/(x^2-4) = 8/(x+2)-(7/(x-2)) // - 8/(x+2)-(7/(x-2))

(2*x)/(x^2-4)-(8/(x+2))+7/(x-2) = 0

(2*x)/(x^2-4)-8*(x+2)^-1+7/(x-2) = 0

(2*x)/(x^2-4)-8/(x+2)+7/(x-2) = 0

(2*x*(x+2)*(x-2))/((x^2-4)*(x+2)*(x-2))+(-8*(x^2-4)*(x-2))/((x^2-4)*(x+2)*(x-2))+(7*(x^2-4)*(x+2))/((x^2-4)*(x+2)*(x-2)) = 0

2*x*(x+2)*(x-2)-8*(x^2-4)*(x-2)+7*(x^2-4)*(x+2) = 0

7*x^3-6*x^3+16*x^2+14*x^2+24*x-28*x-64-56 = 0

x^3+30*x^2-4*x-120 = 0

x^3+30*x^2-4*x-120 = 0

x^3+30*x^2-4*x-120

x^2*(x+30)-4*x-120

x^2*(x+30)-4*(x+30)

(x^2-4)*(x+30)

((x^2-4)*(x+30))/((x^2-4)*(x+2)*(x-2)) = 0

((x^2-4)*(x+30))/((x^2-4)*(x+2)*(x-2)) = 0 // * (x^2-4)*(x+2)*(x-2)

(x^2-4)*(x+30) = 0

( x+30 )

x+30 = 0 // - 30

x = -30

( x^2-4 )

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in { 2} 

x in { -2} 

x = -30

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