Question

How do I simplify this?

Answer 1

\(\Large\frac{5-x}{x^2+3x-4}\div\frac{x^2-2x-15}{x^2+5x+4}\)

Answer 2

Okay. The first thing you need to do is make it into a multiplication problem instead of a division problem. Then you need to break down each polynomial into two parentheticals. For instance, take \[x^{2}+3x-4\] and turn it into (x-3)(x-1). Does that step make sense?

Answer 3

Those subtraction problems should be different but you get the idea of what I'm saying, correct? haha

Answer 4

(x+4)(x-1) is correct

Answer 5

how do I make it into a multiplication problem? @AlmostObvoius sorry, I was afk

Answer 6

When dividing fractions, you multiple by the reciprocal like: \[\frac{ 1 }{ 2 } \div \frac{ 3 }{ 4 }\] becomes \[\frac{ 1 }{ 2 }\times \frac{ 4 }{ 3 }\]

Answer 7

*multiply

Answer 8

Wow, I knew that XD *facepalm*

Answer 9

lol! No worries.

Answer 10

so I have \(\Large\frac{5-x}{(x-1)(x+4)}\times\frac{(x+4)(x+1)}{(x-5)(x+3)}\)

Answer 11

@BlossomCake

Answer 12

o_o I don't think I am the correct person to ask this kind of stuff to. XD

Answer 13

ughhhhhhhhhhhhh

Answer 14

okay

Answer 15

Don't worry. I know someone who can. :D

Answer 16

And he's offline. ;-;

Answer 17

@phi @rvc

Answer 18

who?

Answer 19

I was going to say @dan815 or @rational. :/

Answer 20

Phi is here! :D He can help you. :)

Answer 21

yes, so far so good.
now use "anything divided by itself is 1" (except 0) to simplify

Answer 22

notice you have (x+4) up top and down below. they "cancel" (but make a note: x is not allowed to be -4 , otherwise you would be doing 0/0 and that is not allowed)

Answer 23

so now I have \(\Large\frac{(5-x)(x+1)}{(x-1)(x-5)(x+3)}\). and that means that \(x\cancel=-4\) is a restriction, right?

Answer 24

yes. next notice 5-x and x-5 looks pretty close to the same thing. if you "factor out" -1 from 5-x you get -1(x-5) (notice if you distribute -1*x and -1*-5 you get back -x+5 or 5-x

Answer 25

oh, okay, so it'll be \(\Large\frac{-1(x+1)}{(x-1)(x+3)}\) with \(x\cancel=5\) as a restriction?

Answer 26

yes, but include the first restriction also: \( x \ne -4\)

Answer 27

I know that. Is that it?

Answer 28

or can it be simplified more?

Answer 29

yes. If this is multiple choice, they may show the answer a few different ways, but your way is as good as any , though people might just put a minus sign out front, like this:
\[- \frac{(x+1)}{(x-1)(x+3)} , x\ne -4, x \ne 5\]

Answer 30

it shows different restrictions.. are there any more?

Answer 31

just the obvious ones \( x\ne 1 \) and \( x \ne -3 \)
because otherwise we would be dividing by 0 if x had those values.

Answer 32

that's what I thought, just making sure. Thank you so much for your help!

Answer 33

yw

Answer 34

Can you help with another?

Answer 35

yes

Answer 36

in a new question, right?

Answer 37

ok