8/(x+7)-7/(x+4)=-5

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Solution for 8/(x+7)-7/(x+4)=-5 equation: 


D( x )

x+7 = 0

x+4 = 0

x+7 = 0

x+7 = 0

x+7 = 0 // - 7

x = -7

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x in (-oo:-7) U (-7:-4) U (-4:+oo)

8/(x+7)-(7/(x+4)) = -5 // + 5

8/(x+7)-(7/(x+4))+5 = 0

8/(x+7)-7*(x+4)^-1+5 = 0

8/(x+7)-7/(x+4)+5 = 0

(8*(x+4))/((x+7)*(x+4))+(-7*(x+7))/((x+7)*(x+4))+(5*(x+7)*(x+4))/((x+7)*(x+4)) = 0

8*(x+4)-7*(x+7)+5*(x+7)*(x+4) = 0

5*x^2+x+55*x-17+140 = 0

5*x^2+56*x+123 = 0

5*x^2+56*x+123 = 0

5*x^2+56*x+123 = 0

DELTA = 56^2-(4*5*123)

DELTA = 676

DELTA > 0

x = (676^(1/2)-56)/(2*5) or x = (-676^(1/2)-56)/(2*5)

x = -3 or x = -41/5

(x+41/5)*(x+3) = 0

((x+41/5)*(x+3))/((x+7)*(x+4)) = 0

((x+41/5)*(x+3))/((x+7)*(x+4)) = 0 // * (x+7)*(x+4)

(x+41/5)*(x+3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x+41/5 )

x+41/5 = 0 // - 41/5

x = -41/5

x in { -3, -41/5 }

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