Algebra II

I have some questions on my assignment, if you don't mind could you look over my answers. thanxs!

Find all the numbers that must be excluded from the domain of the rational expression.

x+8/x^2-16, my answer: x cant be -4 or 4

x-3/x^2+11x+24, my answer: x cant be -3 or -8

Simplify the rational expression. Find all the numbers that must be excluded from the domain of the simplified rational expression.

3x+3/15^2+21x+6 I don't understand this one.

Multiply or divide as indicated.

x^2+13x+42/x^2+x-42 * x^2-49/x^2-x-42 I don't understand this one.

(x+7)^2/x-7 / x^2-49/7x-49 This I am not too sure how to do, I know you have to flip the 2nd fraction.

Add or subtract as indicated.

x^2-2x/x^2+6x + x^2+x/x^2+6x I got x-1/x+6

Express the perimeter of the trapezoid as a single rational expression.

These are the rational expressions that are being used: x+6/x+3, 5/x+3, x+1/x+3, 5/x+3. I know you have to add each of the expressions, when I get to the end of working it out, I get x^2+x+6x+6/x+3, but that's not one of my choices. My choices are: a. 2x+17/x+3, b.4x+17/x+3, c.x+17/x+3, and d. x+14.

Simplify the complex rational expression.

4+2/x / x/4+1/8 This one I don't understand how to do it,

"3x+3/15^2+21x+6 I don't understand this one."

First factor it this way:
=1/(5x+2) x cannot be -1 or -2/5

"Multiply or divide as indicated.

x^2+13x+42/x^2+x-42 * x^2-49/x^2-x-42 I don't understand this one. "

I wish you had used brackets, I will assume it was like this:
Multiply or divide as indicated.

(x^2+13x+42)/(x^2+x-42) * (x^2-49)/(x^2-x-42)

Everything here factors:
(x+6)(x+7)/[(x+7)(x-6)] * (x+7)(x-7)/[(x-7)(x+6)]
you calculate the necessary restrictions

"(x+7)^2/x-7 / x^2-49/7x-49 This I am not too sure how to do, I know you have to flip the 2nd fraction."

I am guessing it was like this:
(x+7)^2/(x-7) ÷ (x^2-49)/(7x-49)

= (x+7)^2/(x-7) ÷ (x+7)(x-7)/[7(x-7)]
= (x+7)^2/(x-7) * 7(x-7)/[(x+7)(x-7)]
= 7 because everything cancelled

for the trapezoid question, notice that the denominators are all the same, so just add the numerators to get 2x+17 which is part of your first choice.

I am not going to guess what the last question looks like without using brackets
Retype it using brackets

Add or subtract as indicated

(x^2-2x)/(x^2+6x) + (x^2+x)/(x^2+6x) I got (x-1/x+6)

Simplify the complex rational expression.

(4+2/x) / (x/4+1/8)

Choices are: a.16, b.x/16, c.1, and d.16/x

"(x^2-2x)/(x^2+6x) + (x^2+x)/(x^2+6x) I got (x-1/x+6) "

I got (2x-1)/(x+6), check your numerators

"(4+2/x) / (x/4+1/8) "

common denominator for the top is x,
for the bottom its 8
(4x+2)/x ÷ (2x+1)/8
= (4x+2)/x * 8/(2x+1)
= 16/x

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