What is the simplified form of x+9/4 + x+5/4

- anonymous

What is the simplified form of x+9/4 + x+5/4

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- anonymous

I understand 0% of this lesson... Help?

- anonymous

Sorry, typo.
x+9/x+1 + x-2/5

- anonymous

oh ok thats better

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## More answers

- anonymous

Can you help me?

- anonymous

Here are the choices:

##### 1 Attachment

- mathmale

Look at the two given fractions which are being added together. What is the LCD of this set of 2 fractions? LCD = lowest common denominator.

- anonymous

1?

- mathmale

what does LCD mean to you? Hint: It's not 1.

- anonymous

Lowest common denominator.

- mathmale

Yes, and what does lowest common denominator mean in this context?

- anonymous

Denominator is the lower part of the fraction.

- mathmale

yes, and what does lowest common denominator mean? How do you find the LCD if you are given 2 fractions with different denoms. and are asked to add the fractions together?

- anonymous

I'm not sure off the top of my head what LCD mean in this context.

- mathmale

Better look up Lowest Common Denominator.
Or, given
2/3 + 7/8, find the lcd and then add these fractions together.

- anonymous

LCD means the least common multiple of two numbers.
So, in this question, 5?

- mathmale

Sorry, no. How did you get 5? Try again. what is the LCD of the 2 fractions, \[\frac{ 2 }{ 3 },\frac{ 7 }{ 8 }?\]

- anonymous

Sorry, I ment the question I asked. The LCD of that question is 24.

- anonymous

For mine it should be 5, right?

- mathmale

all right. add the 2 fractions together, please.

- anonymous

9/24, or 3/8?

- anonymous

3/8 being the simplified form?

- mathmale

are you telling me that the sum of 2/3 and 7/8 is 3/8?

- anonymous

Yes. Is that wrong?

- mathmale

definitely, I'm sorry to say.
How long has it been since you last studied "LCD"?

- anonymous

Since 7th grade. I'm in 10th now.

- anonymous

Thats the last time it was reviewed.

- mathmale

Seems as tho' you may need a review. Of course I can help with LCD's, but would prefer not to start from scratch. Since you have internet access, could you look up LCD?

- mathmale

To combine two fractions, you must either have the same denom. in each, or know how to obtain and use the LCD.

- anonymous

Okay

- mathmale

1/3 - (4/3) = ?

- anonymous

1?

- mathmale

No, try again.

- anonymous

:/

- mathmale

sign error

- anonymous

-1?

- mathmale

Better. Right.
find the lcd of 1/x and 2/y

- anonymous

3?

- mathmale

No.
If you're interested, here's the URL of a web site that discusses LCDs and how to find them:
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/equivalent-fractions-pre-alg/v/finding-common-denominators

- mathmale

I'd like to help you, but much prefer you do some reading about LCDs and how to find and use them before we continue. Much material is available on the Internet.

- anonymous

I think I'll just find a different source of help. It might be googling the question since is 5 hours past my teachers hours.

- mathmale

any source of info that works for you would be a good starting point.

- anonymous

I have five other tests that need done before 10 tonight. My time, thats only two hours.

- mathmale

i find the Internet to be a wonderful source of info on the spot.
I very much sympathize, but also wonder how five tests could pile u p into one night.
How long ago were you asked to do these assignments?

- anonymous

the one I'm doing now needed sent in by the 24th of November.

- anonymous

In short, I'm behind.

- mathmale

Surely sounds like it. How did that happen? Do you schedule your study time?

- anonymous

No. Personal issues murdered my sleep schedule and I haven't been able to make it to the online meetings in the mornings.

- mathmale

Let's make the most of the scant time we have. are y ou or are you not going to do some quick research on LCDs on the 'Net?
Exactly what do you hope to get from me, other than answers?

- anonymous

I was hoping to get quick help with small explanations.

- anonymous

Seeing as i asked this over a half hour ago, I assume I'm on the wrong site for that kind of help.

- mathmale

Let's not be sarcastic. I object to having to explain concepts from scratch when you could reasonably be expected to have studied and practiced the basics.

- anonymous

Like I said, my schedule's been tight due to personal issues. I would study the stuff harder if I had the time for it.

- mathmale

You must have the same denominator in 2 fractions BEFORE you can add or subtract them. That's the principle.
The next quesion is HOW DO YOU FIND THE LCD? what do you remember?
I'm sorry about your having personal issues to deal with.

- mathmale

Add:\[\frac{ 3 }{ 7 }+\frac{ 2 }{ 5 }\]

- mathmale

to find the lcd, multiply the 7 and 5 together.

- anonymous

3/35 + 2/35?

- anonymous

21/35 + 14/35?

- mathmale

The first fraction is 3/7. If you mult. the denom. by 7, you must also mult the numerator by 7. Do that now, please.

- mathmale

Much b etter.

- anonymous

Then simplify?

- mathmale

Looking at the second fraction, whose den. is 5, mult both numerator and den. by 7 .

- anonymous

14/35?

- mathmale

\[\frac{ 3 }{ 7 }+\frac{ 2 }{ 5 }\]

- mathmale

Yes. You've mult both num. and den. of the 2nd fraction by 7. I made a mistake on the first fract. Mult both its num. and den. by 5, please.

- anonymous

10/25?

- mathmale

5 times 3 is 10?

- anonymous

Sorry, 15

- anonymous

15/35

- mathmale

better.
Now you have \[\frac{ 15 }{ 35 }+\frac{ 14 }{ 35 }\]

- mathmale

What is the LCD?

- anonymous

the LCD is 35.

- mathmale

Good. Now becasue you have the same den. in both fract., you can add the numerators to get the final answer (the sum)

- mathmale

Do so, please.

- anonymous

The simplified answer should be 29/35, right?

- mathmale

Can't be simplified. Yes, the final answer is 29/35. Congrats.

- mathmale

Now, find the LCD, use it and then add together \[\frac{ 3 }{ 7 }+\frac{ 2 }{ x }\]

- mathmale

the LCD is ... ?

- anonymous

7?

- mathmale

How did you get that? Have you used multiplication here?

- anonymous

7 * x = 7 since I don't know what x represents.

- mathmale

In this case you MUST mult two quantities together. Yes, the LCD is 7x.

- anonymous

Okay.

- mathmale

Given \[\frac{ 3 }{ 7 }+\frac{ 2 }{ x }\]

- mathmale

by what quantity must you mult. the num. and the den. of the first fract. ? why?

- anonymous

Is this cross multiplication?

- mathmale

No. focus on the 1st fract. Determine by what quant. you must mult. its num. and den.

- anonymous

By x, right?

- mathmale

Exactly. Do so, please.

- anonymous

3x / 7x?

- mathmale

very nice.
By what quant. must you mult num. and den. of the 2nd fract?

- anonymous

By x as well?

- mathmale

No. What's the LCD here?\[\frac{ 3 }{ 7 }+\frac{ 2 }{ x }\]

- anonymous

7x

- anonymous

So, 2x/7x?

- mathmale

Thus, mult the num and den of the 2nd fract by what quantity?

- anonymous

By x.

- mathmale

No, we've already used x to modify the 1st fract.
Now we are modifying the 2nd fract.

- anonymous

Then, 7?

- mathmale

\[\frac{ 3 }{ 7 }+\frac{ 2 }{ x }\]

- mathmale

Yes. Do so, please.

- anonymous

14/7x

- mathmale

Cool.

- mathmale

Then you have \[\frac{ 3 }{ 7 }+\frac{ 2 }{ x }\]

- anonymous

2x/7x + 14x/7x is what we have now.

- mathmale

or equivalently,
\[\frac{ 3x }{ 7x}+\frac{ 14 }{ 7x }\]

- anonymous

17x/7x?

- mathmale

please complete the addition. Note that that's (3x) / (7x), not (2x) / (7x).

- mathmale

How'd you get 17x?

- mathmale

Remember, this is addition.

- anonymous

3x + 14 = 17x

- mathmale

not so.
does 1 dime plus 1 quarter equal 2 quarters?

- mathmale

Try again.

- mathmale

3x and 17 are NOT "like terms," so you cannot simplify their sum. You muxst write
"3x+17" and let it go at that.
So, your final answer is ... what?

- anonymous

3x+14
------
7x

- mathmale

Beautiful.

- anonymous

Okay.

- mathmale

My understanding is that you want to add: x+9/x+1 + x-2/5

- anonymous

Should I send a picture of the problem?

- mathmale

Better expressed as\[\frac{ x+9 }{ x+1 }+\frac{ x+2 }{ 5 }\]

- mathmale

Is that correct?

- anonymous

No. x - 2

- mathmale

\[\frac{ x+9 }{ x+1 }+\frac{ x-2 }{ 5 }\]

- mathmale

better?

- anonymous

Yes.

- mathmale

Good. What is the lcd?

- mathmale

think back to what you did earlier!

- anonymous

x+5?

- mathmale

Never add or subtract the dens. Always mult or div. It's almost always mult.
Try again.
LCD= ?

- mathmale

\[\frac{ x+9 }{ x+1 }+\frac{ x-2 }{ 5 }\]

- anonymous

5(x+1)?

- mathmale

Exactly. What did you do to the x+1 and the 5?

- anonymous

I'm not sure. I just looked at my answers and picked the ones that i didn't add together to get.

- mathmale

Oh, shoot. correct response: I multiplied the 2 different denoms. together to obtain the LCD>

- mathmale

The LCD here is .... ?

- anonymous

x + 6?

- anonymous

If its not the first answer to that question.

- mathmale

Repeat: Do NOT add or subtract the dens. Do not add 1 and 5.
You are allowed ONLY to mult or div. NOT to add or subtract.

- mathmale

What is the LCD here?

- anonymous

Then, 5(x+1)

- mathmale

So much better. You got that before, but forgot.

- anonymous

Okay.

- mathmale

\[\frac{ x+9 }{ x+1 }+\frac{ x-2 }{ 5 }\]

- mathmale

If you mult the den of the 1st fract by 5, you must also mult the num of the first fract by 5.

- mathmale

Do that now, please.

- mathmale

Just show that you have a product; you don't yet have to multiply out the product.

- anonymous

Okay.

- mathmale

\[\frac{5( x+9) }{ 5*(x+1) }+\frac{ x-2 }{ 5 }\]

- anonymous

x-10/5(x+1)

- mathmale

Now mult num and den of the 2nd fract by (x+1).

- mathmale

Thx for trying but x-10/5(x+1) is not correct.

- mathmale

Mult (x+9) by 5.

- mathmale

Must use parentheses. Picky, picky.

- anonymous

(x+45)

- mathmale

\frac{5( x+9) }{ 5*(x+1) }+\frac{ x-2 }{ 5 }\[\frac{5( x+9) }{ 5*(x+1) }+\frac{ x-2 }{ 5 }\]

- mathmale

Put parentheses around the x-2. Multiply (x+2) by (x+1).

- mathmale

Mult that 5 by (x+1). Use parentheses liberally.

- mathmale

Sorry, is it x-1? You fix it for me, please.

- anonymous

(x-2)5(x+1)?

- mathmale

\[\frac{5( x+9) }{ 5*(x+1) }+\frac{ (x-2)(x+1) }{ 5*(x+1) }\]

- anonymous

Okay.

- anonymous

So, add it together?

- mathmale

Now you have to multiply out 5(x+9) Likewise, you have to mult out (x-2)(x+1).
Finally, you have to combine all the like terms.
And then y ou're DONE>
sorry I have to get off the 'Net NOW, but if you have further questions I'll be back in about an hour.
Thanks for your persistence.

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