Question

(x+3)(x+1)=((4-x)(x+3))/2

Answer 1

(x+3)(x+1)=((4-x)(x+3))/2
(x+3)(x+1)-((4-x)(x+3))/2=0
(x+3)((x+1)-(4-x)/2)=0
х=-3
2(x+1)=4-x
2x+2=4-x
3x=2
x=2/3
ответ 2/3  -3

Answer 2

Let's simplify the given equation:

(x + 3)(x + 1) = ((4 - x)(x + 3))/2

Expanding the left side:

x^2 + x + 3x + 3 = ((4 - x)(x + 3))/2

Combining like terms:

x^2 + 4x + 3 = ((4 - x)(x + 3))/2

Expanding the right side:

x^2 + 4x + 3 = (4x + 12 - x^2 - 3x)/2

Multiplying both sides by 2 to eliminate the fraction:

2(x^2 + 4x + 3) = 4x + 12 - x^2 - 3x

Expanding and rearranging the terms:

2x^2 + 8x + 6 = 4x + 12 - x^2 - 3x

Combining like terms:

2x^2 + 8x + 6 = -x^2 + x + 12

Moving all terms to one side:

3x^2 + 7x - 6 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:

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

Setting each factor equal to zero:

3x - 2 = 0 or x + 3 = 0

Solving these equations:

3x = 2 or x = -3

Dividing both sides by 3 in the first equation:

x = 2/3

Therefore, the solutions to the equation (x + 3)(x + 1) = ((4 - x)(x + 3))/2 are x = 2/3 and x = -3.