(2x+3)/3 + (x-1)/2 = (-x + 3)/6. To solve for x .

This is a linear equation.

The LCM of the denominators is 6.

To solve the equation , we multiply both sides by the LCM of the demominators.

6 {(2x+3)/3 + (x-1)/2} = 6{(-x + 3)/6}

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

4x+6 +3x-3 = -x+3.

7x+3 = -x+3

7x+x = 0

8x = 0

x = 0

Therefore x = 0.

First thing, to determine x, we'll have to calculate the least common denominator of the 3 ratios.

LCD = 2*3

LCD = 6

Now, we'll multiply the first ratio by 2 and the second ratio by 3. The 3rd ratio has the denominator 6, so it won't be multiplied.

2(2x+3)/6 + 3(x-1)/6 = (-x + 3)/6

We ca re-write the expression without denominator:

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

We'll remove the brackets:

4x + 6 + 3x - 3 = -x + 3

We'll move the terms from the right side to the left side:

4x + 6 + 3x - 3 + x - 3 = 0

We'll combine and eliminate like terms:

8x = 0

We'll divide by 8:

x = 0

**The solution of the equation is x = 0.**