Question

Can someone check my Algebra 2 answers please? I fan and medal!!

1. What is the simplified form of (x+1/x^2+x-6)/(x^2+5x+4/x-2)
Answer: 1/(x+4)(x-2)
2. What is the simplified form of (2/x^2+x)-(1/x)
Answer: 3-x/x(x-1)
3. What is the simplified form of (3/2x-5)+(21/8x^2-14x-15)
Answer: 6(2x+5)/(2x-5)(4x+3)
4. What is the simplified form of (3/x^2)/(1/x^3)
Answer: 1/3x
5. What is the simplified form of (15xy^2/x^2+5x+6)/(5x^2y/2x^2+7x+3)
Answer: x(x-2)/3y(2x-1)
6. What are the discountinuities of the function f(x)=(x^2+5x+6)/(2x+16)
Answer: x does not equal -8

Answer 1

7. What are the vertical asymptotes of the function f(x)=(4x+8)/(x^2+3x-4)
Answer: x=-1 and x=-4

Answer 2

I am getting a different answer for 1.

Answer 3

What did you get for number one?

Answer 4

\[\frac{1}{(x+3)(x+4)}\].

Getting a different answer for #2 also. I don't want to end up giving all the answers.

Answer 5

Okay I understand. Could you explain how you did number one?

Answer 6

\[
\frac{ x+1}{x^2+x-6} \div \frac{x^2+5x+4}{x-2} = \\
\frac{(x+1)}{(x+3)(x-2)} \div \frac{(x+4)(x+1)}{(x-2)} = \\
\frac{(x+1)}{(x+3)(x-2)} \times \frac{(x-2)}{(x+4)(x+1)} = \\
\frac{\cancel{(x+1)}}{(x+3)\cancel{(x-2)}} \times \frac{\cancel{(x-2)}}{(x+4)\cancel{(x+1)}} = \frac{1}{(x+3)(x+4)}\\
\]

Answer 7

Okay I see what I did wrong. Thank you!

Answer 8

I redid number 2. This time I got (1-x)/x(x+1) is that correct?

Answer 9

Yes.