Question

simplify the expression:

x+8/x^2-5x-6 + x+1/x^2-4x-5

Answer 1

damn

Answer 2

Is that supposed to be\[\frac{x+8}{x^2-5x-6} + \frac{x+1}{x^2-4x-5}\]by any chance?

Answer 3

you really need to put parentheses around the numerator and denominator if you're going to write it all on one line like that:
(x+8)/(x^2-5x-6) + (x+1)/(x^2-4x-5)

What you've written is really
\[x + \frac{8}{x^2}-5x-6 + x + \frac{1}{x^2}-4x-5\]but I'm confident that isn't what you intend

Answer 4

Anyhow, to simplify this, you'll want to factor both denominators, then get a common denominator so you can combine the fractions

Answer 5

hey whpalmer4, can you help me?

Answer 6

is that not what I'm doing?

Answer 7

oh no that's someone eles question. mine is:

One railroad track was laid out on the line y = 8x - 2 by the engineers in charge. Which of the following lines could have been the other parallel track?

A. y = 2x - 8
B. y = -⅛x + 3
C. y = 4 + 8x
D. 2y = 8x + 3

Answer 8

thanks @whpalmer4

Answer 9

@sagek54321 very rude to inject your question in someone else's question like that. Tag me on your question and I'll have a look when I get a minute

Answer 10

Im sorry I didnt mean to be rude i just thought that you could help me here.. im new to this site

Answer 11

@whpalmer4 yes it is suppoe to look like this:

\[\frac{ x+8 }{ x^2-5x-6 }+\frac{ x+1 }{ x^2-4x-5 }\]

Answer 12

no problem, I told you what the etiquette is, now it's up to you :-) to tag me, just put @whpalmer4 in the body of a response to your question

Answer 13

okay, can you factor the two denominators?

Answer 14

yes I can

Answer 15

So I got this when I factored the denominators.. would the x-5 on the left side and right side both cancel each other?

\[\frac{ x+8 }{(x-1)(x-5) }+\frac{ x+1 }{ (x+1)(x-5) }\]

Answer 16

That's not quite a correct factoring, I'm afraid...

\[(x-1)(x-5) = x^2 - 5x - 1x + 5 = x^2 -6x + 5\]which is not the denominator of either fraction

Answer 17

Also, you'll have a different factoring for each fraction, as the denominators are different

Answer 18

no I typed it wrong on the left side it's suppose to be (x-1)(x-6) sorry I can't read my own hand writting tonight

Answer 19

\[(x-1)(x-6) = x^2 - 6x -1x + 6 = x^2 -7x + 6\]Try again? :-)

Answer 20

how about \((x-6)(x+1)\)?

Answer 21

Yeah I caught that as I was looking it over again :P

Answer 22

\[\frac{(x+8)}{(x+1)(x-6)} + \frac{(x+1)}{(x+1)(x-5)}\]now looks like you need to multiply the left fraction by \(\dfrac{(x-5)}{(x-5)}\); what do you need to do for the right fraction?

Answer 23

wouldn't the (x+1) on the right cancel top and bottom? right?

Answer 24

It would, if you canceled it, but you don't have to, and don't want to here. You want to get the common denominator for both fractions, then add the numerators

Answer 25

ok so then I would need to multiply the right side by \[\frac{ (x-6) }{ (x-6) }\]

Answer 26

Yep.

Answer 27

okay thank you.. I'll tag you if i need any extra help if that is okay?

Answer 28

this is the final answer I got.
\[\frac{ 2x^2-1x-45 }{ (x-5)(x+1)(x-6) }\]

Answer 29

Close but not quite. Check your work for the numerator again

Answer 30

ok

Answer 31

okay i rechecked my work...

\[\frac{ 2x^2-2x-46 }{ (x-5)(x+1)(x-6) }\]

Answer 32

@whpalmer4

Answer 33

Now we're talking! Though you could write the numerator as \(2(x^2-x-23)\). As there's no real definition of what it means to simplify, it's hard to argue with either one.

Answer 34

okay thank you so much for all the awesome help!!!

Answer 35

You're welcome.