(7x)/(7x+7)=((-4x)/(5x+5))+(9x-72)/(x+1)

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Solution for (7x)/(7x+7)=((-4x)/(5x+5))+(9x-72)/(x+1) equation:


D( x )

x+1 = 0

5*x+5 = 0

7*x+7 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

5*x+5 = 0

5*x+5 = 0

5*x+5 = 0 // - 5

5*x = -5 // : 5

x = -5/5

x = -1

7*x+7 = 0

7*x+7 = 0

7*x+7 = 0 // - 7

7*x = -7 // : 7

x = -7/7

x = -1

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

(7*x)/(7*x+7) = (-4*x)/(5*x+5)+(9*x-72)/(x+1) // - (-4*x)/(5*x+5)+(9*x-72)/(x+1)

(7*x)/(7*x+7)-((-4*x)/(5*x+5))-((9*x-72)/(x+1)) = 0

(7*x)/(7*x+7)+4*x*(5*x+5)^-1-((9*x-72)/(x+1)) = 0

(7*x)/(7*x+7)+(4*x)/(5*x+5)+(-1*(9*x-72))/(x+1) = 0

(7*x*(5*x+5)*(x+1))/((7*x+7)*(5*x+5)*(x+1))+(4*x*(7*x+7)*(x+1))/((7*x+7)*(5*x+5)*(x+1))+(-1*(9*x-72)*(7*x+7)*(5*x+5))/((7*x+7)*(5*x+5)*(x+1)) = 0

7*x*(5*x+5)*(x+1)+4*x*(7*x+7)*(x+1)-1*(9*x-72)*(7*x+7)*(5*x+5) = 0

63*x^3-315*x^3+126*x^2+1890*x^2+63*x+4725*x+2520 = 0

2016*x^2-252*x^3+4788*x+2520 = 0

2016*x^2-252*x^3+4788*x+2520 = 0

252*(8*x^2-x^3+19*x+10) = 0

8*x^2-x^3+19*x+10 = 0

{ 1, -1, 2, -2, 5, -5, 10, -10 }

1

x = 1

8*x^2-x^3+19*x+10 = 36

1

-1

x = -1

8*x^2-x^3+19*x+10 = 0

-1

x+1

9*x-x^2+10

8*x^2-x^3+19*x+10

x+1

x^3+x^2

9*x^2+19*x+10

-9*x^2-9*x

10*x+10

-10*x-10

0

9*x-x^2+10 = 0

DELTA = 9^2-(-1*4*10)

DELTA = 121

DELTA > 0

x = (121^(1/2)-9)/(-1*2) or x = (-121^(1/2)-9)/(-1*2)

x = -1 or x = 10

x in { -1, 10, -1}

252*(x+1)^2*(x-10) = 0

(252*(x+1)^2*(x-10))/((7*x+7)*(5*x+5)*(x+1)) = 0

(252*(x+1)^2*(x-10))/((7*x+7)*(5*x+5)*(x+1)) = 0 // * (7*x+7)*(5*x+5)*(x+1)

252*(x+1)^2*(x-10) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-10 )

x-10 = 0 // + 10

x = 10

x in { -1}

x = 10

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