Question

i just need adding these rational expressions

Answer 1

\[\frac{ x-5 }{ 5x } + \frac{ x+1 }{ 2x }\]

Answer 2

Hi! Have you had practice with other rational expressions? Like, easier ones? Because they can probably relate well to this problem.

Answer 3

What do you think would be a good first step?

Answer 4

finding a commoin denominator?

Answer 5

Sounds good to me! Do you have any ideas for that?

Answer 6

10? idk

Answer 7

Looks good to me, with an \(x\) attached! \(10x\), yep! Because \(5x\) goes into it and \(2x\) goes into it.

Now you have to start the next step.
You don't want to change either term's amount. But you want to change how they look. So what you do, essentially, is multiply by \(1\) so nothing changes. But \(1=\dfrac{2}{2}=\dfrac{3}{3}=\dfrac{\text{anything}}{\text{that same anything}}\), right?

Answer 8

So what do you have to multiply \(5x\) by to get to \(10x\). That's the next step. After that, it's multiplying like... I'll do the first term. You have to multiply \(5x\) by \(2\). So, I multiply the whole term by \(1=\dfrac{2}{2}\). I'm not changing the amount! But it does make this convenient. Then we have
\(\dfrac{x-5}{5x}\times\dfrac{2}{2}\).

Do you want to do the next term?

Answer 9

um. hold up for the next step would the \[\frac{ x-5 }{ 5x } equal \frac{ x^2-10 }{ 10x } ? \]
just checking if im understanding this right

Answer 10

It's always good to check.
\(\dfrac{ x-5 }{ 5x } =\dfrac{\color{#00CC33}{2} x^\color{red}{\cancel 2}-10 }{ 10x } \)

Answer 11

Then it's good! :)

Answer 12

The numerator is like...
\(\left( x-5\right)\times2\\=
\left( x\times2-5\times2\right)\\=
\left(2x-10\right)\\=2x-10
\)

Answer 13

oh ok i see what i did wrong in that one

Answer 14

and the denominator is like
\(5x\times2\\=5\times x\times2\\=
5\times2\times x\\=
10\times x\\=
10x
\)

Answer 15

Cool! :)

Answer 16

That's all we can do with that term for now. We can't add the rational terms until they have the same denominator. So we should move on to the next one. Would you like to try to tackle that?

Answer 17

yeah! so im guessing since they have to both have the same denominator. so doing so it would be \[\frac{ 2x-10 }{ 10x } + \frac{ 2x+5 }{ 10x }\]

Answer 18

Check where you have the \(2x\) in the term on the right!

Answer 19

so itd equal \[\frac{ 4x-5 }{ 10x }\] how am i doing so far?

Answer 20

Easy mistake... You were just multiplying by \(2\) so much!

Answer 21

:)

Answer 22

oh hold up

Answer 23

Haha, you did see to multiply by \(5\), so you're getting the concept. Little math errors like that wind up even in professors' lessons.

Answer 24

\[\frac{ 2x-10 }{ 10x } + \frac{ 2x+10 }{ 10x } = \frac{ 4x }{ 10 }\]

Answer 25

4x/10x

Answer 26

Let's go back to \(\dfrac{x+1}{2x}\times\dfrac{5}{5}\) for a moment and check that out.

Answer 27

That's the term that was on the right side in the very beginning. And we multiply like that to get the denominator of \(10x\).

Answer 28

oh wow completely forgot about the 5..

Answer 29

:) The one issue with math on OpenStudy is that this format of post after post isn't very organized for math. Heheh

Answer 30

haha yeah, so it would be \[\frac{ 5x+1 }{ 10x } \] \[+ \frac{ 2x-10 }{ 10x } = \frac{ 7x-5 }{ 10x }\]
alright hows that

Answer 31

\[\frac{ 5x+1\color{#00CC33}{\times5} }{ 10x }\color{#00CC33}{=\frac{5x+5}{10x}}\]Practice makes better! I have to go step by step when I do math, or I'll do things wrong. It's just a matter of finding something that works for you!
You can look at the numerator alone, if that helps.
\((x+1)\times 5=5x\times5\)

Answer 32

uhhh hah i see i see

Answer 33

Good! So what we did so far is this:
\(
\dfrac{ x-5 }{ 5x } + \dfrac{ x+1 }{ 2x }\\=
\dfrac{ x-5 }{ 5x }\times\dfrac{2}{2} \quad+\quad \dfrac{ x+1 }{ 2x }\times\dfrac{5}{5}\\=
\dfrac{ 2x-10 }{ 10x } + \dfrac{ 5x+5 }{ 10x }
\)

Answer 34

And I saw you add them like normal before, just with one wrong number, so I'll add these now since you know how.

Answer 35

\(
\dfrac{ 2x-10 }{ 10x } + \dfrac{ 5x+5 }{ 10x }\\=
\dfrac{(2x-10)+(5x+5)}{10x}\\=
\dfrac{2x-10+5x+5}{10x}\\=
\dfrac{7x-5}{10x}
\)

Does that look good to you?

Answer 36

Yes it does! TY

Answer 37

You're welcome! You did a lot of it, congrats! Will your teacher be satisfied with that? Or will he or she want more simplification?

Answer 38

no thats perfect ill be able to right down the steps i took now that i understamd

Answer 39

Okay then! Do you think you have any more questions on that, then?

I had already started changing how it looks.. So it's not necessary, but if you're interested, here's another way to write the same thing.
\(
\dfrac{7x-5}{10x}\\=
\dfrac{7x}{10x}-\dfrac{5}{10x}\\=
\dfrac{7}{10}-\dfrac{1}{2}x
\)

Answer 40

Both ways look nice, and that's all that matters.

Answer 41

Heheh..

Answer 42

oh could you help me with another problem. its similar to this one but for subtraction

Answer 43

Yeah, and I'm sure you can do it! Post it as a separate question, please, if you don't mind! Much less messy.

Answer 44

yeah sure