# What is x if 72/(3x+3) -x=3?

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To find x if 72/(3x+3)-x = 3.

We first multiply by 3x+3 both sides of the equation:

72 -x(3x+3) = 3(3x+3).

72 - 3x^2-3x = 9x+9.

Subtract 72-3x^2-3x from both sides:

0 = 9x+9 -72+3x^2+3x.

0 = 3x^2+12x-63.

We didvide by 3 both sides:

0 = x^2+4x-21.

We proceed to factorise the right side:

0 = x^2+7x -3x-21.

0 = x(x+7)-3(x+7).

0 = (x+7)(x-3) .

We equate the factor to zero:

x+7 = 0, x-3 = 0.

So x= -7 or x = 3.

First, we'll factorize by 3 the denominator of the ratio 72/(3x+3) = 72/3(x+1).

Then, we'll divide by 3 both numerator and denominator of the ratio:

72/3(x+1) = 24/(x+1)

We'll have to multiply both sides by the denominator x+1.

24(x + 1)/ (x + 1) - x(x+1) = 3(x+1)

We'll simplify and we'll move all terms to one side:

24 - x(x+1) - 3(x+1) = 0

24 - x^2 - x - 3x - 3 = 0

We'll combine like terms:

- x^2 - 4x + 21 = 0

We'll multiply by -1:

x^2 + 4x - 21 = 0

We'll apply quadratic formula:

x1 = [-4+sqrt(16+84)]/2

x1 = (-4+10)/2

x1 = 3

x2 = (-4-10)/2

x2 = -7