7y/(7y+7)+(7y-17)/(6y+6)=(6y+1)/(y+1)

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Solution for 7y/(7y+7)+(7y-17)/(6y+6)=(6y+1)/(y+1) equation:


D( y )

6*y+6 = 0

y+1 = 0

7*y+7 = 0

6*y+6 = 0

6*y+6 = 0

6*y+6 = 0 // - 6

6*y = -6 // : 6

y = -6/6

y = -1

y+1 = 0

y+1 = 0

y+1 = 0 // - 1

y = -1

7*y+7 = 0

7*y+7 = 0

7*y+7 = 0 // - 7

7*y = -7 // : 7

y = -7/7

y = -1

y in (-oo:-1) U (-1:+oo)

(7*y)/(7*y+7)+(7*y-17)/(6*y+6) = (6*y+1)/(y+1) // - (6*y+1)/(y+1)

(7*y)/(7*y+7)+(7*y-17)/(6*y+6)-((6*y+1)/(y+1)) = 0

(7*y)/(7*y+7)+(7*y-17)/(6*y+6)+(-1*(6*y+1))/(y+1) = 0

(7*y*(6*y+6)*(y+1))/((7*y+7)*(6*y+6)*(y+1))+((7*y-17)*(7*y+7)*(y+1))/((7*y+7)*(6*y+6)*(y+1))+(-1*(6*y+1)*(7*y+7)*(6*y+6))/((7*y+7)*(6*y+6)*(y+1)) = 0

7*y*(6*y+6)*(y+1)+(7*y-17)*(7*y+7)*(y+1)-1*(6*y+1)*(7*y+7)*(6*y+6) = 0

91*y^3-252*y^3+63*y^2-546*y^2-147*y-336*y-119-42 = 0

-161*y^3-483*y^2-483*y-161 = 0

-161*y^3-483*y^2-483*y-161 = 0

-161*(y^3+3*y^2+3*y+1) = 0

y^3+3*y^2+3*y+1 = 0

{ 1, -1 }

1

y = 1

y^3+3*y^2+3*y+1 = 8

1

-1

y = -1

y^3+3*y^2+3*y+1 = 0

-1

y+1

y^2+2*y+1

y^3+3*y^2+3*y+1

y+1

-y^3-y^2

2*y^2+3*y+1

-2*y^2-2*y

y+1

-y-1

0

y^2+2*y+1 = 0

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

DELTA = 0

y = -2/(1*2)

y = -1 or y = -1

y in { -1, -1, -1}

-161*(y+1)^3 = 0

(-161*(y+1)^3)/((7*y+7)*(6*y+6)*(y+1)) = 0

(-161*(y+1)^3)/((7*y+7)*(6*y+6)*(y+1)) = 0 // * (7*y+7)*(6*y+6)*(y+1)

-161*(y+1)^3 = 0

y+1 = 0 // - 1

y = -1

y in { -1}

y belongs to the empty set

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