# Thread: How to complete these problems?

1. ## How to complete these problems?

I'm having difficulties solving the following problems, I would very much appreciate it if someone could show me how to solve them step-by-step.

Add or Subtract as indicated and simplify.

14. (x)/(x +3) + (3)/(x +3)

15. (a^2 - 1)/(a - 1) - (a - 1)/(a + 1)

16. (1)/(x) - (3)/(x+2) - (6)/(x^2 + 2x)

Multiply or divide as indicated and simplify.

17. (x^2 + x - 20)/(x^2 - 16) times (x^2 - 25)/(x - 5)

18. (x + 2)/(x^2 + 2x + 1) divided by (x^2 - 4)/(x + 1)

2. Originally Posted by Quincy Goss
I'm having difficulties solving the following problems, I would very much appreciate it if someone could show me how to solve them step-by-step.

Add or Subtract as indicated and simplify.

14. (x)/(x +3) + (3)/(x +3)

15. (a^2 - 1)/(a - 1) - (a - 1)/(a + 1)

16. (1)/(x) - (3)/(x+2) - (6)/(x^2 + 2x)

Multiply or divide as indicated and simplify.

17. (x^2 + x - 20)/(x^2 - 16) times (x^2 - 25)/(x - 5)

18. (x + 2)/(x^2 + 2x + 1) divided by (x^2 - 4)/(x + 1)
HI

(14) $\frac{x}{x+3}+\frac{3}{x+3}=\frac{x+3}{x+3}=1$

(15) $\frac{a^2-1}{a-1}-\frac{a-1}{a+1}$

$=\frac{(a+1)(a-1)}{a-1}-\frac{a-1}{a+1}$

$=\frac{(a+1)^2-(a-1)}{a+1}$

$
=\frac{a^2+2a+1-a+1}{a+1}
$

Then continue simplifying , i think you can try (16)

For (17) , $\frac{x^2+x-20}{x^2-16}\times\frac{x^2-25}{x-5}$

$\frac{(x+5)(x-4)}{(x+4)(x-4)}\times\frac{(x+5)(x-5)}{x-5}$

do some appropriate cancellings , then simplify .

Now try (18) .

3. Thanks so much!

4. Originally Posted by Quincy Goss
I'm having difficulties solving the following problems, I would very much appreciate it if someone could show me how to [simplify] them step-by-step.
Ouch! They were supposed to have covered this material in the book and / or in class before assigning homework on them!

To learn, in general, how to work these exercises, try some online lessons: