3/(x-5)+7/(x+2)=5/(x^2-3x-10)

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Solution for 3/(x-5)+7/(x+2)=5/(x^2-3x-10) 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)

3/(x-5)+7/(x+2) = 5/(x^2-(3*x)-10) // - 5/(x^2-(3*x)-10)

3/(x-5)+7/(x+2)-(5/(x^2-(3*x)-10)) = 0

3/(x-5)+7/(x+2)-5*(x^2-3*x-10)^-1 = 0

3/(x-5)+7/(x+2)-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)*(x-5) = 0

3/(x-5)+7/(x+2)-5/((x+2)*(x-5)) = 0

(3*(x+2))/((x-5)*(x+2))+(7*(x-5))/((x-5)*(x+2))-5/((x-5)*(x+2)) = 0

3*(x+2)+7*(x-5)-5 = 0

10*x-29-5 = 0

10*x-34 = 0

(10*x-34)/((x-5)*(x+2)) = 0

(10*x-34)/((x-5)*(x+2)) = 0 // * (x-5)*(x+2)

10*x-34 = 0

10*x-34 = 0 // + 34

10*x = 34 // : 10

x = 34/10

x = 17/5

x = 17/5

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