4/(x-4)+3/(x-4)=2/(x+7)(x-4)

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Solution for 4/(x-4)+3/(x-4)=2/(x+7)(x-4) 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)

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

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

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

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

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

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

7*x-2*x^2+16*x-32+49 = 0

23*x-2*x^2+17 = 0

23*x-2*x^2+17 = 0

23*x-2*x^2+17 = 0

DELTA = 23^2-(-2*4*17)

DELTA = 665

DELTA > 0

x = (665^(1/2)-23)/(-2*2) or x = (-665^(1/2)-23)/(-2*2)

x = (665^(1/2)-23)/(-4) or x = (665^(1/2)+23)/4

(x-((665^(1/2)-23)/(-4)))*(x-((665^(1/2)+23)/4)) = 0

((x-((665^(1/2)-23)/(-4)))*(x-((665^(1/2)+23)/4)))/((x-4)*(x+7)) = 0

((x-((665^(1/2)-23)/(-4)))*(x-((665^(1/2)+23)/4)))/((x-4)*(x+7)) = 0 // * (x-4)*(x+7)

(x-((665^(1/2)-23)/(-4)))*(x-((665^(1/2)+23)/4)) = 0

( x-((665^(1/2)+23)/4) )

x-((665^(1/2)+23)/4) = 0 // + (665^(1/2)+23)/4

x = (665^(1/2)+23)/4

( x-((665^(1/2)-23)/(-4)) )

x-((665^(1/2)-23)/(-4)) = 0 // + (665^(1/2)-23)/(-4)

x = (665^(1/2)-23)/(-4)

x in { (665^(1/2)+23)/4, (665^(1/2)-23)/(-4) }

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