Question

Help with expressions?

Answer 1

\[\frac{ 5x }{ 3x+5 } + \frac{ x }{ x+1 } +\frac{ x }{ x-1 }\]

Answer 2

@wio

Answer 3

make like terms via the denominator

Answer 4

Okay you need to find LCD.

Answer 5

Alrighty... Let's see.

Answer 6

Is it 15?

Answer 7

No, it would just be: \[
(3x+5)(x+1)(x-1)
\]

Answer 8

Ohh okay.

Answer 9

Now you need each term to have that in the denominator.

Answer 10

So..
\[\frac{ 5x+x+x }{ (3x+5)(x+1)(x-1) }\]

Answer 11

I feel like that's wrong.

Answer 12

No, one term at a time.

Answer 13

YOU SHOULD NOW THIS

Answer 14

\[\frac{ 5x }{ 3x+5 } \cdot \frac{ (x+1)(x-1) }{ (x+1)(x-1) } = \frac{(5x)(x+1)(x-1)}{(3x+5)(x+1)(x-1)}\]

Answer 15

Ohhh okay! See I thought that but it seemed too complex.

Answer 16

What next? Simplify?

Answer 17

No, each term needs to be converted like this.

Answer 18

Then you may add them

Answer 19

What do you mean converted? I thought that was the outcome of finding the LCD.

Answer 20

omg wio do u ever get a brake?

Answer 21

This guy works so hard on here. He honestly deserves to be paid.

Answer 22

yesh u are right

Answer 23

We converted the first term.
Now we need to convert this second term:\[ \frac{ x }{ x+1 } \]

Answer 24

So we multiply top and bottom by \((3x+5)(x-1)\)?

Answer 25

Do I use FOIL?

Answer 26

No, not yet.

Answer 27

Okay. So
\[\frac{ x(3x+5)(x-1) }{ x(3x+5)(x-1)(x+1) }\]

Answer 28

Actually, you should get:\[\small \frac{ 5x(x+1)(x-1) }{ (3x+5)(x+1)(x-1) } + \frac{ x(3x+5)(x-1) }{ (x+1)(3x+5)(x-1) } +\frac{ x(3x+5)(x+1) }{ (x-1)(3x+5)(x+1) }\]

Answer 29

Oh geez. Alright!

Answer 30

Yes, it's a bit crazy

Answer 31

I have no idea where to go from here. There's just so many numbers.

Answer 32

Well, since they have a common denominator, you can add the numerators.

Answer 33

Just focus on the top parts for now.

Answer 34

:D

Answer 35

Focus on this:\[5x(x+1)(x-1) + x(3x+5)(x-1)+ x(3x+5)(x+1)\]

Answer 36

You have to foil them out, then you can combine like terms.

Answer 37

Alright. Is it \[x(11x^2+10x-5)\]

Answer 38

Yes, that is correct.

Answer 39

http://www.wolframalpha.com/input/?i=5x(x%2B1)(x%E2%88%921)%2Bx(3x%2B5)(x%E2%88%921)%2Bx(3x%2B5)(x%2B1)

Answer 40

So we have: \[
\frac{11x^3+10x^2-5x}{(3x+5)(x+1)(x-1)}
\]

Answer 41

They might want you to expand the bottom.

Answer 42

Alright. Is that it?

It doesn't specify to expand.

Answer 43

Well, expanded form typically is considered to be more simplified.

Answer 44

But I think it is enough.

Answer 45

Alright. Thank you so much!! I really appreciate you guys at OS!