Question

PLEASE HELPPPPPP SIMPLIFING? and state any restrictions on the variables. x/4x-8 - x+1/x^2+2x-8

i know that the simplified answer is x+2/4(x+4) but i don't know how to get that answer or what the restrictions on the variables are.

Answer 1

To find the restrictions, you find all of the values of x that make any denominator equal 0. You do this *before* you simplify — even if you simplify away a term from the denominator that makes it look like there isn't a division by 0, the restriction still remains.

You haven't written your expression correctly, but I'll guess that you meant

\[\frac{x}{4x-8} - \frac{x+1}{x^2+2x-8}\]

Answer 2

if you are going to do without the spatial clues, you need to add parentheses to show the precise expression. You could have written that as
\[(x)/(4x-8) - (x+1)/(x^2+2x-8)\]

By the rules of operator precedence, what you wrote is actually
\[\frac{x}{4x} - 8 - x + \frac{1}{x^2+2x-8}\]

Answer 3

To simplify this, I would start by factoring the denominators. What do you get if you factor both denominators completely?

Answer 4

sorry, i didn't know if i should have wrote it with parenthesis or not because there isn't any on the worksheet. but yeah, i meant the first thing you put.

Answer 5

Now you do. One down, only a bazillion more OpenStudy users to go :-)

Answer 6

So, can you factor those denominators?

Answer 7

haha. and how do i do that

Answer 8

wait,would this be the first thing i do x/[4(x − 2)] − (x + 1)/[(x + 4)(x − 2)]

Answer 9

yes! Now it's easy to see what to do to get a common denominator, right?

Answer 10

wait, can i show you my full problem then can you tell me if i got it right?

Answer 11

cause i didn't think i did cause of the restrictions stuff

Answer 12

x/[4(x − 2)] − (x + 1)/[(x + 4)(x − 2)]
[x(x + 4)]/[4(x + 4)(x − 2)] − [4(x + 1)]/[4(x + 4)(x − 2)]
[x(x+ 4) − 4(x + 1)]/[4(x + 4)(x − 2)]
[x^2 + 4x − 4x − 4]/[4(x + 4)(x − 2)]
[x^2 − 4]/[4(x + 4)(x − 2)]
[(x + 2)(x − 2)]//[4(x + 4)(x − 2)]

Answer 13

Okay, that's correct. Now, what are the values of \(x\) that give you a denominator of 0?

Answer 14

After you've done that, you can simplify that last fraction some more.

Answer 15

x=2 ????

Answer 16

Yes. Any others?

Answer 17

-4 maybe??

Answer 18

Maybe? There's no maybe, only yes or no :-)

Answer 19

\[x^2+2x-8\]\[(-4)^2+2(-4)-8 = 16-8-8 = 0\]That looks like a clear yes to me!

Answer 20

yay!! thank you :)

Answer 21

so the restrictions are 2 and -4 right?/

Answer 22

you're welcome.

Answer 23

yes, the restricted values are \(x = 2\) and \(x=-4\)