simplify each expression.

1. 6/2b - 1 minus 4/b - 1
2. n-6/2n + 2 plus 4n/3
3. 4/6x^3 - 12x^2 minus x - 3/6x^3 - 12x^2

please explain how to do these!! thanks

To simplify these expressions, we will combine like terms and perform any necessary operations.

1. 6/2b - 1 - 4/b - 1:
First, we need to simplify each fraction by finding a common denominator. The common denominator here is 2b.

6/2b - 1 becomes 3/b - 1.
-4/b - 1 remains the same.

Next, we combine the two fractions by subtracting them:
(3/b - 1) - (4/b - 1)
= 3/b - 1 - 4/b + 1

Now, we can combine like terms, which are the fractions with the same denominator:
= (3 - 4)/b + (1 - 1)
= (-1)/b

So, the simplified expression is -1/b.

2. (n-6)/2n + 2 + 4n/3:
First, we need to simplify each fraction by finding a common denominator. The common denominator here is 6n.

(n-6)/2n + 2 becomes (3n-18)/6n + 2/1.
4n/3 remains the same.

Next, we combine the fractions:
(3n-18)/6n + 2/1 + 4n/3

To add these fractions, we need to find a common denominator, which is 6n. We can multiply (3n-18) by 3 to get the common denominator:
[ (3n-18)(3) + 2(6n) + 4n(2n) ] / (6n)

Simplifying further:
(9n-54 + 12n + 8n^2) / (6n)
= (8n^2 + 21n - 54) / (6n)

So, the simplified expression is (8n^2 + 21n - 54) / (6n).

3. 4/6x^3 - 12x^2 - x - 3/6x^3 - 12x^2:
First, we need to simplify each fraction by finding a common denominator. The common denominator here is 6x^3.

4/6x^3 - 12x^2 becomes 2/3x^3 - 12x^2.
-3/6x^3 - 12x^2 becomes -1/2x^3 - 12x^2.

Next, we combine the fractions by subtraction:
(2/3x^3 - 12x^2) - (-1/2x^3 - 12x^2)

To subtract fractions, we need to find a common denominator, which is 6x^3:
[ (2/3x^3)(2x^3)/(2x^3) - (12x^2)(2x^3)/(2x^3) ] - [ (-1/2x^3)(3x^3)/(3x^3) - (12x^2)(3x^3)/(3x^3) ]

Simplifying further:
(4x^6 - 24x^5) / (6x^3) - (-3x^6 + 36x^5) / (6x^3)
= (4x^6 - 24x^5 + 3x^6 - 36x^5) / (6x^3)

Combine like terms:
(7x^6 - 60x^5) / (6x^3)

So, the simplified expression is (7x^6 - 60x^5) / (6x^3).