(x/(x^2-14x+49))-(1/(2x+14))=(x/(2x^2-98))

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Solution for (x/(x^2-14x+49))-(1/(2x+14))=(x/(2x^2-98)) equation:


D( x )

2*x^2-98 = 0

2*x+14 = 0

x^2-(14*x)+49 = 0

2*x^2-98 = 0

2*x^2-98 = 0

2*x^2 = 98 // : 2

x^2 = 49

x^2 = 49 // ^ 1/2

abs(x) = 7

x = 7 or x = -7

2*x+14 = 0

2*x+14 = 0

2*x+14 = 0 // - 14

2*x = -14 // : 2

x = -14/2

x = -7

x^2-(14*x)+49 = 0

x^2-(14*x)+49 = 0

x^2-14*x+49 = 0

x^2-14*x+49 = 0

DELTA = (-14)^2-(1*4*49)

DELTA = 0

x = 14/(1*2)

x = 7 or x = 7

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

x/(x^2-(14*x)+49)-(1/(2*x+14)) = x/(2*x^2-98) // - x/(2*x^2-98)

x/(x^2-(14*x)+49)-(1/(2*x+14))-(x/(2*x^2-98)) = 0

x/(x^2-14*x+49)-(2*x+14)^-1-(x/(2*x^2-98)) = 0

x/(x^2-14*x+49)-1/(2*x+14)+(-1*x)/(2*x^2-98) = 0

x^2-14*x+49 = 0

x^2-14*x+49 = 0

x^2-14*x+49 = 0

DELTA = (-14)^2-(1*4*49)

DELTA = 0

x = 14/(1*2)

x = 7 or x = 7

(x-7)^2 = 0

x/((x-7)^2)-1/(2*x+14)+(-1*x)/(2*x^2-98) = 0

(x*(2*x+14)*(2*x^2-98))/((x-7)^2*(2*x+14)*(2*x^2-98))+(-1*(x-7)^2*(2*x^2-98))/((x-7)^2*(2*x+14)*(2*x^2-98))+(-1*x*(x-7)^2*(2*x+14))/((x-7)^2*(2*x+14)*(2*x^2-98)) = 0

x*(2*x+14)*(2*x^2-98)-1*(x-7)^2*(2*x^2-98)-1*x*(x-7)^2*(2*x+14) = 0

2*x^4-2*x^4+56*x^3+14*x^3-196*x^2+98*x^2-2744*x-686*x+4802 = 0

70*x^3-98*x^2-3430*x+4802 = 0

70*x^3-98*x^2-3430*x+4802 = 0

14*(5*x^3-7*x^2-245*x+343) = 0

5*x^3-7*x^2-245*x+343 = 0

{ 1, -1, 7, -7, 49, -49, 343, -343 }

1

x = 1

5*x^3-7*x^2-245*x+343 = 96

1

-1

x = -1

5*x^3-7*x^2-245*x+343 = 576

-1

7

x = 7

5*x^3-7*x^2-245*x+343 = 0

7

x-7

5*x^2+28*x-49

5*x^3-7*x^2-245*x+343

x-7

35*x^2-5*x^3

28*x^2-245*x+343

196*x-28*x^2

343-49*x

49*x-343

0

5*x^2+28*x-49 = 0

DELTA = 28^2-(-49*4*5)

DELTA = 1764

DELTA > 0

x = (1764^(1/2)-28)/(2*5) or x = (-1764^(1/2)-28)/(2*5)

x = 7/5 or x = -7

x in { -7, 7/5, 7}

14*(x+7)*(x-7/5)*(x-7) = 0

(14*(x+7)*(x-7/5)*(x-7))/((x-7)^2*(2*x+14)*(2*x^2-98)) = 0

(14*(x+7)*(x-7/5)*(x-7))/((x-7)^2*(2*x+14)*(2*x^2-98)) = 0 // * (x-7)^2*(2*x+14)*(2*x^2-98)

14*(x+7)*(x-7/5)*(x-7) = 0

( x+7 )

x+7 = 0 // - 7

x = -7

( x-7/5 )

x-7/5 = 0 // + 7/5

x = 7/5

( x-7 )

x-7 = 0 // + 7

x = 7

x in { -7}

x in { 7}

x = 7/5

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