3/(7x+21)=4/(x+3)-5/7

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Solution for 3/(7x+21)=4/(x+3)-5/7 equation: 


D( x )

7*x+21 = 0

x+3 = 0

7*x+21 = 0

7*x+21 = 0

7*x+21 = 0 // - 21

7*x = -21 // : 7

x = -21/7

x = -3

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x in (-oo:-3) U (-3:+oo)

3/(7*x+21) = 4/(x+3)-(5/7) // - 4/(x+3)-(5/7)

3/(7*x+21)-(4/(x+3))+5/7 = 0

3/(7*x+21)-4*(x+3)^-1+5/7 = 0

3/(7*x+21)-4/(x+3)+5/7 = 0

(3*7*(x+3))/(7*(7*x+21)*(x+3))+(-4*7*(7*x+21))/(7*(7*x+21)*(x+3))+(5*(7*x+21)*(x+3))/(7*(7*x+21)*(x+3)) = 0

3*7*(x+3)-4*7*(7*x+21)+5*(7*x+21)*(x+3) = 0

35*x^2-175*x+210*x-525+315 = 0

35*x^2+35*x-210 = 0

35*x^2+35*x-210 = 0

35*(x^2+x-6) = 0

x^2+x-6 = 0

DELTA = 1^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

35*(x+3)*(x-2) = 0

(35*(x+3)*(x-2))/(7*(7*x+21)*(x+3)) = 0

(35*(x+3)*(x-2))/(7*(7*x+21)*(x+3)) = 0 // * 7*(7*x+21)*(x+3)

35*(x+3)*(x-2) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -3} 

x = 2

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