Answer:
1.
= 
2.
= 
3.
= 
4.
= 
Step-by-step explanation:
1. 
Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)

Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.
2. 
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)
Putting factors

Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.
3. 
Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)
Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)
Putting factors

Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)


Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.
4. 
Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

Converting ÷ sign into multiplication we will take reciprocal of the second term

Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.
Answer:
The first piece is 7 ft long, the second piece is 12 ft long, and the third piece is 13 ft long
Step-by-step explanation:
Let x represent the length of the first piece.
Since the second piece is 5 ft longer than the first, it can be represented by x + 5
Since the third piece is 1 ft longer than the second, it can be represented by x + 6
Create an equation that adds all of these terms up to 32, and solve for x
(x) + (x + 5) + (x + 6) = 32
3x + 11 = 32
3x = 21
x = 7
So, the first piece is 7 ft long.
Using the expressions we created, solve for the lengths of the second and third pieces.
x + 5
7 + 5 = 12
x + 6
7 + 6 = 13
The first piece is 7 ft long, the second piece is 12 ft long, and the third piece is 13 ft long
Negative bc negative times positive is negative