1/(x-7)+1/(x-8)=15/56

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Solution for 1/(x-7)+1/(x-8)=15/56 equation: 


D( x )

x-7 = 0

x-8 = 0

x-7 = 0

x-7 = 0

x-7 = 0 // + 7

x = 7

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:7) U (7:8) U (8:+oo)

1/(x-7)+1/(x-8) = 15/56 // - 15/56

1/(x-7)+1/(x-8)-(15/56) = 0

1/(x-7)+1/(x-8)-15/56 = 0

(1*56*(x-8))/(56*(x-7)*(x-8))+(1*56*(x-7))/(56*(x-7)*(x-8))+(-15*(x-7)*(x-8))/(56*(x-7)*(x-8)) = 0

1*56*(x-8)+1*56*(x-7)-15*(x-7)*(x-8) = 0

112*x-15*x^2+225*x-840-840 = 0

337*x-15*x^2-1680 = 0

337*x-15*x^2-1680 = 0

337*x-15*x^2-1680 = 0

DELTA = 337^2-(-1680*(-15)*4)

DELTA = 12769

DELTA > 0

x = (12769^(1/2)-337)/(-15*2) or x = (-12769^(1/2)-337)/(-15*2)

x = 112/15 or x = 15

(x-112/15)*(x-15) = 0

((x-112/15)*(x-15))/(56*(x-7)*(x-8)) = 0

((x-112/15)*(x-15))/(56*(x-7)*(x-8)) = 0 // * 56*(x-7)*(x-8)

(x-112/15)*(x-15) = 0

( x-112/15 )

x-112/15 = 0 // + 112/15

x = 112/15

( x-15 )

x-15 = 0 // + 15

x = 15

x in { 112/15, 15 }

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