How do you simplify these rational expressions?

Question

1. 16+4x / 4x

2. c-2 / c(squared) - 4

3. -(b+1) / b (squared) + 6b + 5

Also, there aren't supposed to be parenthesis around the numbers, so don't factor it.

Answer 1

Some things to note. Always use parentheses to clear up confusion. I'll explain why below.

1. 16 + 4x / 4x
I assume you mean:
(16+4x) / 4x
= 4(4 + x) / 4x
= (4 + x) / x

2. c-2 / c(squared) - 4
I assume you mean:
(c - 2) / (c^2 - 4)
The denominator is the difference of squares:
(c - 2) / (c - 2)(c + 2)
= 1 / (c + 2)

3. -(b+1) / b (squared) + 6b + 5
I assume you mean:
-(b + 1) / (b^2 + 6b + 5)
= -(b + 1) / (b + 5)(b + 1)
= -1 / (b + 5)

Edit: Are you certain that there are not supposed to be parentheses? When they're written on paper, the above questions don't need parentheses, because they physically sit above and below the dividing line. When writing online like this, you don't have that luxury, so you add parentheses.

You can see how easily you can factor the three expressions above. I'll demonstrate what they are like without parentheses:

1. 16+4x / 4x <== The 4x cancel out, leaving 1.
= 16 + 1
= 17

2. c - 2/c^2 - 4 <== Multiply by c^2 to remove the denominator:
c^3 - 4c^2 - 2
This is not easily factorable.

3. -(b + 1)/b^2 +6b + 5 <== Multiply by b^2 to remove the denominator:
6b^3 + 5b^2 - b - 1
This is not easily factorable.

I really think the parentheses apply here.

Answer 2

1.
(16+4x) / 4x
= 4(4+x)/4x

= (4+x)/x


2.

(c-2) / (c^2 - 4)

= (c-2) / (c-2)(c+2) {difference of two squares}

= 1/(c-2)

Whoops

I mean
= 1/(c+2)

(DOH!)


3.

-(b+1) / (b^2 + 6b + 5)

= -(b+1) / (b+1)(b+5)

= -1/(b+5)