(n+3)/(3n-5)=n+6

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Solution for (n+3)/(3n-5)=n+6 equation: 


D( n )

3*n-5 = 0

3*n-5 = 0

3*n-5 = 0

3*n-5 = 0 // + 5

3*n = 5 // : 3

n = 5/3

n in (-oo:5/3) U (5/3:+oo)

(n+3)/(3*n-5) = n+6 // - n+6

(n+3)/(3*n-5)-n-6 = 0

(n+3)/(3*n-5)+(-n*(3*n-5))/(3*n-5)+(-6*(3*n-5))/(3*n-5) = 0

n-n*(3*n-5)-6*(3*n-5)+3 = 0

6*n-3*n^2-18*n+3+30 = 0

33-3*n^2-12*n = 0

33-3*n^2-12*n = 0

3*(11-n^2-4*n) = 0

11-n^2-4*n = 0

DELTA = (-4)^2-(-1*4*11)

DELTA = 60

DELTA > 0

n = (60^(1/2)+4)/(-1*2) or n = (4-60^(1/2))/(-1*2)

n = (2*15^(1/2)+4)/(-2) or n = (4-2*15^(1/2))/(-2)

3*(n-((2*15^(1/2)+4)/(-2)))*(n-((4-2*15^(1/2))/(-2))) = 0

(3*(n-((2*15^(1/2)+4)/(-2)))*(n-((4-2*15^(1/2))/(-2))))/(3*n-5) = 0

(3*(n-((2*15^(1/2)+4)/(-2)))*(n-((4-2*15^(1/2))/(-2))))/(3*n-5) = 0 // * 3*n-5

3*(n-((2*15^(1/2)+4)/(-2)))*(n-((4-2*15^(1/2))/(-2))) = 0

( n-((2*15^(1/2)+4)/(-2)) )

n-((2*15^(1/2)+4)/(-2)) = 0 // + (2*15^(1/2)+4)/(-2)

n = (2*15^(1/2)+4)/(-2)

( n-((4-2*15^(1/2))/(-2)) )

n-((4-2*15^(1/2))/(-2)) = 0 // + (4-2*15^(1/2))/(-2)

n = (4-2*15^(1/2))/(-2)

n in { (2*15^(1/2)+4)/(-2), (4-2*15^(1/2))/(-2) }

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