Find the LCD of both fractions, then simplify the expression. Assume that no denominator equals zero. 5/3x^2y - 4/6xy^3

- Bananas1234

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- Bananas1234

@JoannaBlackwelder

- Bananas1234

@Nnesha

- JoannaBlackwelder

The LCD is finding the smallest denominator that makes them both the same.

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## More answers

- JoannaBlackwelder

Do you have any ideas of how to start doing that?

- Bananas1234

how do i find that?

- Bananas1234

not sure, sorry

- JoannaBlackwelder

Ok, the two denominators are|dw:1433440171339:dw|

- JoannaBlackwelder

I mean... |dw:1433440214478:dw|

- Bananas1234

ok

- JoannaBlackwelder

If we multiply the left one by 2, we get a common coefficient|dw:1433440278787:dw|

- JoannaBlackwelder

Do you see how that gives us a common coefficient of 6?

- JoannaBlackwelder

|dw:1433440359049:dw|

- Bananas1234

yes, because 2 times 3 is 6?

- JoannaBlackwelder

Right.

- JoannaBlackwelder

And we have 2 x's on the left, but only 1 on the right.

- JoannaBlackwelder

So we need to multiply the right side by x to make the number of x's the same

- JoannaBlackwelder

|dw:1433440468526:dw|

- Bananas1234

i see

- JoannaBlackwelder

:-) How do you think we can make the number of y's the same?

- Bananas1234

times it by y?

- JoannaBlackwelder

Close. That would give us:|dw:1433440631552:dw|

- JoannaBlackwelder

So the numbers of y's still aren't quite the same.

- Bananas1234

they arent?

- Bananas1234

ok whats next

- JoannaBlackwelder

It looks like we have 2 y's on the left, but 3 on the left.

- Bananas1234

i see

- Bananas1234

you mean 3 on the right?

- JoannaBlackwelder

Yeah, sorry.

- Bananas1234

ok

- JoannaBlackwelder

So, we need one more y on the left.

- Bananas1234

ok, so do we mulitply again?

- JoannaBlackwelder

Yep

- Bananas1234

|dw:1433440911998:dw|

- JoannaBlackwelder

Yep, great! So, are the denominators the same now?

- Bananas1234

yes

- JoannaBlackwelder

Great! So, in the full problem, how do we make that both denominators?

- Bananas1234

|dw:1433441111648:dw|

- Bananas1234

Like that?

- JoannaBlackwelder

But we can't just change the denominators. We have to also change the numerators to keep everything balanced.

- Bananas1234

oh, i forgot about that

- Bananas1234

ow do we do that?

- Bananas1234

how*

- JoannaBlackwelder

What do we need to multiply by the first denominator to get it to be our LCM?

- JoannaBlackwelder

*LCD

- Bananas1234

not sure, sorry.

- JoannaBlackwelder

|dw:1433441688086:dw|

- Bananas1234

what do i put in the (?)?

- Bananas1234

@JoannaBlackwelder

- JoannaBlackwelder

What did we multiply by to get the LCD of the left side?

- Bananas1234

by y?

- JoannaBlackwelder

Was that all?

- Bananas1234

i think so....

- JoannaBlackwelder

No, |dw:1433442752287:dw| so we need to multiply the left fraction on top and bottom by 2y^2

- Bananas1234

oh

- JoannaBlackwelder

|dw:1433442908806:dw|

- JoannaBlackwelder

Can you simplify?

- Bananas1234

how do i simplify??

- JoannaBlackwelder

Multiply

- Bananas1234

multiply the 5 by the 2y^2?

- JoannaBlackwelder

Yep

- Bananas1234

10y^2/6x^2y^3?

- JoannaBlackwelder

Yep, great! How about the other fraction?

- Bananas1234

|dw:1433443839427:dw| Like this??

- Bananas1234

so 8y2/12xy^5?

- Bananas1234

8y^2/12xy^5 @JoannaBlackwelder

- Bananas1234

is that all i need to do? @JoannaBlackwelder

- Bananas1234

please reply i have 20 mins to get this done :( @JoannaBlackwelder

- JoannaBlackwelder

Sorry, I was doing some online tutoring. But no, we didn't multiply by 2y^2 on the right fraction to get the LCD.

- Bananas1234

ok

- JoannaBlackwelder

|dw:1433445935170:dw|

- JoannaBlackwelder

We need to multiply the right fraction by x to make common denominators.

- Bananas1234

i got that part

- JoannaBlackwelder

|dw:1433446083616:dw|

- Bananas1234

i see

- JoannaBlackwelder

:-)

- JoannaBlackwelder

|dw:1433446145225:dw|

- JoannaBlackwelder

So, now we can subtract the numerators, and the denominators stay the same.

- JoannaBlackwelder

So, what does that give us?

- Bananas1234

6y^2x?

- JoannaBlackwelder

No, I mean for the whole fraction.

- Bananas1234

im having a hard time subtracting the bottom

- JoannaBlackwelder

It stays the same. Doesn't subtract.

- Bananas1234

ohh i see

- JoannaBlackwelder

|dw:1433446648437:dw|

- Bananas1234

so,6y^2x/6x^2y^3

- JoannaBlackwelder

No, only like terms can add.

- Bananas1234

ok

- Bananas1234

so its 10y^2 - 4x/6x^2y^3 is that all??

- JoannaBlackwelder

Well, we can simplify a bit by factoring out a 2

- Bananas1234

what 2?

- Bananas1234

i do have to get this turned in now, if i don't i will get a 0

- Bananas1234

the 2 on 6 and 10??

- JoannaBlackwelder

Yes, and the 4

- JoannaBlackwelder

You can turn it in like that. You should get partial credit

- Bananas1234

ok, but if i were to do it some other time what can i do?

- JoannaBlackwelder

|dw:1433447702331:dw|

- Bananas1234

ok, thank you for all of your help, sorry that took so long.

- JoannaBlackwelder

And the twos cancel out. |dw:1433447840612:dw|

- JoannaBlackwelder

You're welcome :-)

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