(5/x-2)+(2/x+7)=(17/(x+7)(x-2))

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Solution for (5/x-2)+(2/x+7)=(17/(x+7)(x-2)) equation: 


D( x )

x+7 = 0

x = 0

x+7 = 0

x+7 = 0

x+7 = 0 // - 7

x = -7

x = 0

x = 0

x in (-oo:-7) U (-7:0) U (0:+oo)

5/x+2/x-2+7 = (17/(x+7))*(x-2) // - (17/(x+7))*(x-2)

5/x-((17/(x+7))*(x-2))+2/x-2+7 = 0

5/x-17*(x-2)*(x+7)^-1+2/x-2+7 = 0

(-17*(x-2))/(x+7)+5/x+2/x-2+7 = 0

(-17*x*(x-2))/(x*(x+7))+(5*(x+7))/(x*(x+7))+(2*(x+7))/(x*(x+7))+(-2*x*(x+7))/(x*(x+7))+(7*x*(x+7))/(x*(x+7)) = 0

5*(x+7)-17*x*(x-2)+2*(x+7)-2*x*(x+7)+7*x*(x+7) = 0

7*x^2-17*x^2-2*x^2+39*x+2*x-14*x+49*x+14+35 = 0

7*x^2-17*x^2-2*x^2+41*x-14*x+49*x+49 = 0

7*x^2-19*x^2+27*x+49*x+49 = 0

76*x-12*x^2+49 = 0

76*x-12*x^2+49 = 0

76*x-12*x^2+49 = 0

DELTA = 76^2-(-12*4*49)

DELTA = 8128

DELTA > 0

x = (8128^(1/2)-76)/(-12*2) or x = (-8128^(1/2)-76)/(-12*2)

x = (8*127^(1/2)-76)/(-24) or x = (-8*127^(1/2)-76)/(-24)

(x-((8*127^(1/2)-76)/(-24)))*(x-((-8*127^(1/2)-76)/(-24))) = 0

((x-((8*127^(1/2)-76)/(-24)))*(x-((-8*127^(1/2)-76)/(-24))))/(x*(x+7)) = 0

((x-((8*127^(1/2)-76)/(-24)))*(x-((-8*127^(1/2)-76)/(-24))))/(x*(x+7)) = 0 // * x*(x+7)

(x-((8*127^(1/2)-76)/(-24)))*(x-((-8*127^(1/2)-76)/(-24))) = 0

( x-((-8*127^(1/2)-76)/(-24)) )

x-((-8*127^(1/2)-76)/(-24)) = 0 // + (-8*127^(1/2)-76)/(-24)

x = (-8*127^(1/2)-76)/(-24)

( x-((8*127^(1/2)-76)/(-24)) )

x-((8*127^(1/2)-76)/(-24)) = 0 // + (8*127^(1/2)-76)/(-24)

x = (8*127^(1/2)-76)/(-24)

x in { (-8*127^(1/2)-76)/(-24), (8*127^(1/2)-76)/(-24) }

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