Question

Can someone help me simplify complex rational expressions?

Answer 1

Can you give an example of what you're working on?

Answer 2

Simplify ((1/x) + (1/y)) / (x+y)

Answer 3

Notice that your adding x to y in two different places (in different forms) and try to find a way to get them to cancel. Multiply your 1/x by y/y and your 1/y by x/x. ( you. can do this because y/y = 1 and multiply by 1 doesn't change anything.) now add those two fractions together now that they have the same common denominator. Next, remember that x + y (on the bottom of your original fraction) is actually over 1. Now you have one fraction divided by another. To do that, flip over the bottom one and multiply. Your x + y will cancel and you'll be left with 1/xy

Answer 4

okay that helped for that one but how would i do harder ones like ((x/3) - 1) / (x-3)

Answer 5

That problem is actually very similar. Start by Turning 1 into 3/3 and getting so you have 2 fractions on the top with a common denominator that you can add into one fraction

Answer 6

so it would then be ((x-3/3)) / x-3 ?

Answer 7

Perfect! Now take the bottom of your whole fraction and remember that it has a silent 1 under it, so you really have [(x-3)/3]/[(x-3)/1] then take flip your bottom fraction and multiply by your top

Answer 8

so the x-3's would cross out leaving me 1/3?

Answer 9

You got it! : )

Answer 10

Thank you so much! I have a couple more problems if you could help me but if you don't want to or your'e busy then that's fine.

Answer 11

I'm here. What you got?

Answer 12

((1+ 1/x)) / ((3- 1/x))

Answer 13

Stat by turning both of your whole numbers into fractions, getting common denominators, and adding.

Answer 14

1 will equal x/x and 3 will be 9/3

Answer 15

Oops typo

Answer 16

3 will be 3x/x

Answer 17

so the answer is x/4x?

Answer 18

Not what I got, did you have [(x+1)/x]/[(3x-1)/x]?

Answer 19

I might have thrown you off with that mistake I made up there

Answer 20

after I get that I do the flip over and multiple thing?

Answer 21

Yup, don't try to simplify too much. The x's will cancel, but the x+1 and the 3x-1 will not

Answer 22

so it's x+1/3x-1?

Answer 23

On the nose! : )

Answer 24

awesome :) so I started a different problem and got to the flip and multiple part. I got
(1/x+1) times ((x-3)(x+1)+(x-3))/1 and I crossed out the x+1's

Answer 25

You still there?

Answer 26

Oops sorry stepped out for a bit

Answer 27

That looks a little complicated. What was the starting problem?

Answer 28

(1/(x+1)) / (1/(x^2-2x-3)) + (1/x-3))

Answer 29

Is that last part 1/(x+3) or (1/x) + 3

Answer 30

Except its a minus, this is kinda hard on an ipad

Answer 31

1/(x+3)

Answer 32

Ok, very sorry, my Internet died, but I figured it out

Answer 33

You were exactly right when you factored. Then you need to get a common denomination on those two fractions on the bottom of your big fraction. Since you already factored you can see that all you need to do is multiply (x+1)/(x+1) times your 1/(x-3)

Answer 34

okay and I have one more but I need to go eat dinner so if you could just kind of give a brief description on how to do it and if you're on when I'm done I can ask questions if I need to.
(x-(x/x+3)) / x+2

Answer 35

Ok I did it but it' s not quick to explain one. I'll type it up, and if you have to leave before I'm done that's ok

Answer 36

okay. Thank you so much for all your help. I really appreciate it

Answer 37

First multiply your x by (x+3)/(x+3)

Answer 38

Then multiply your x(x+3) out so you have x^2 + 3x

Answer 39

Now, when you add those fractions with the common denominator (x+3) you'll end up with x^2 + 3x -x

Answer 40

That simplifies to x^2 + 2x

Answer 41

Now you need to re factor it so you have x(x+2)

Answer 42

So you'll have [(x(x+2))/(x+3)]/[(x+2)/1]

Answer 43

When you flip and multiply your (x+2) will cancel and you'll be left with x/(x+3)

Answer 44

It was fun working with you. Good luck!