adding and subtracting rational expressions and finding LCD

[hunterjumper46]

Please Help!

1. 4 4
--------- _ --------
x-8 x+8


2. 15x x+1
------------ _ -----------
x^2+ 5x x+5


3. x+3 x-2
------- + --------
x+7 3x+5

4. x 4
------= ------- + 2
x+4 x+4

5. 2 7 1
--- = ------- _ -------
3 3x-12 x-4

6. 1 1 10
------ + ------ = ---------
x-3 x+3 x^2-9

Thanks!

Ashley

 

[jonboy]

Ashley you can't have multiple spacing to make fractions like that so it's very hard to tell what you mean. Please pull down the forum help and go on Karl's Notes to learn how to input fractions.

 

[stapel]

Your formatting is unclear; in what follows, I will state what I have guessed to be your meaning. If I have guessed incorrectly, please forgive my confusion and reply with clarification. Thank you.

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

What are the instructions for this? Are you supposed to "simplify"? "Find the domain"? "Graph"? "State the least common denominator"? "Convert to that common denominator"? Or something else?

Are you able at least to get started? If so, please reply showing your work. If not, please specify that you are requesting links to lessons.

2) (15x) / (x^2 + 5x) - (x + 1) / (x + 5)

3) (x + 3) / (x + 7) + (x - 2) / (3x + 5)

Same comments on (2) and (3) as for (1).

4) x / (x + 4) = 4 / (x + 4) + 2

I will guess that the instructions were along the lines of "solve the equation, and check". A good first step would be to multiply through by the common denominator, obtaining:

. . . . .x = 2x + 12

Then solve the linear equation, and check that the solution works in the original rational equation.

5) 2 / 3 = 7 / (3x - 12) - 1 / (x - 4)

6) 1 / (x - 3) + 1 / (x + 3) = 10 / (x^2 - 9)

Exercises (5) and (6) work similarly to (4).

Please reply with correction or confirmation. Thank you.

Eliz.

P.S. Welcome to FreeMathHelp!