(x)/(x^2-3x-10)=(2)/(x-5)-(4)/(x+2)

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Solution for (x)/(x^2-3x-10)=(2)/(x-5)-(4)/(x+2) equation: 


D( x )

x-5 = 0

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

x+2 = 0

x-5 = 0

x-5 = 0

x-5 = 0 // + 5

x = 5

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

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

x^2-3*x-10 = 0

x^2-3*x-10 = 0

DELTA = (-3)^2-(-10*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)

x = 5 or x = -2

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x in (-oo:-2) U (-2:5) U (5:+oo)

x/(x^2-(3*x)-10) = 2/(x-5)-(4/(x+2)) // - 2/(x-5)-(4/(x+2))

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

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

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

x^2-3*x-10 = 0

x^2-3*x-10 = 0

x^2-3*x-10 = 0

DELTA = (-3)^2-(-10*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)

x = 5 or x = -2

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

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

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

4*(x-5)-2*(x+2)+x = 0

4*x-x-20-4 = 0

3*x-24 = 0

(3*x-24)/((x+2)*(x-5)) = 0

(3*x-24)/((x+2)*(x-5)) = 0 // * (x+2)*(x-5)

3*x-24 = 0

3*x-24 = 0 // + 24

3*x = 24 // : 3

x = 24/3

x = 8

x = 8

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