3/(x+5)-4/(x+2)=5/(x^2+7x+10)

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Solution for 3/(x+5)-4/(x+2)=5/(x^2+7x+10) equation: 


D( x )

x^2+7*x+10 = 0

x+5 = 0

x+2 = 0

x^2+7*x+10 = 0

x^2+7*x+10 = 0

x^2+7*x+10 = 0

DELTA = 7^2-(1*4*10)

DELTA = 9

DELTA > 0

x = (9^(1/2)-7)/(1*2) or x = (-9^(1/2)-7)/(1*2)

x = -2 or x = -5

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

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

3/(x+5)-(4/(x+2)) = 5/(x^2+7*x+10) // - 5/(x^2+7*x+10)

3/(x+5)-(4/(x+2))-(5/(x^2+7*x+10)) = 0

3/(x+5)-4*(x+2)^-1-5*(x^2+7*x+10)^-1 = 0

3/(x+5)-4/(x+2)-5/(x^2+7*x+10) = 0

x^2+7*x+10 = 0

x^2+7*x+10 = 0

x^2+7*x+10 = 0

DELTA = 7^2-(1*4*10)

DELTA = 9

DELTA > 0

x = (9^(1/2)-7)/(1*2) or x = (-9^(1/2)-7)/(1*2)

x = -2 or x = -5

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

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

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

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

-x-14-5 = 0

-x-19 = 0

(-x-19)/((x+5)*(x+2)) = 0

(-x-19)/((x+5)*(x+2)) = 0 // * (x+5)*(x+2)

-x-19 = 0

-x-19 = 0 // + 19

-x = 19 // * -1

x = -19

x = -19

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