Bananas1234
  • Bananas1234
Find the LCD of both fractions, then simplify the expression. Assume that no denominator equals zero. 5/3x^2y - 4/6xy^3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Bananas1234
  • Bananas1234
@JoannaBlackwelder
Bananas1234
  • Bananas1234
@Nnesha
JoannaBlackwelder
  • JoannaBlackwelder
The LCD is finding the smallest denominator that makes them both the same.

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More answers

JoannaBlackwelder
  • JoannaBlackwelder
Do you have any ideas of how to start doing that?
Bananas1234
  • Bananas1234
how do i find that?
Bananas1234
  • Bananas1234
not sure, sorry
JoannaBlackwelder
  • JoannaBlackwelder
Ok, the two denominators are|dw:1433440171339:dw|
JoannaBlackwelder
  • JoannaBlackwelder
I mean... |dw:1433440214478:dw|
Bananas1234
  • Bananas1234
ok
JoannaBlackwelder
  • JoannaBlackwelder
If we multiply the left one by 2, we get a common coefficient|dw:1433440278787:dw|
JoannaBlackwelder
  • JoannaBlackwelder
Do you see how that gives us a common coefficient of 6?
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433440359049:dw|
Bananas1234
  • Bananas1234
yes, because 2 times 3 is 6?
JoannaBlackwelder
  • JoannaBlackwelder
Right.
JoannaBlackwelder
  • JoannaBlackwelder
And we have 2 x's on the left, but only 1 on the right.
JoannaBlackwelder
  • JoannaBlackwelder
So we need to multiply the right side by x to make the number of x's the same
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433440468526:dw|
Bananas1234
  • Bananas1234
i see
JoannaBlackwelder
  • JoannaBlackwelder
:-) How do you think we can make the number of y's the same?
Bananas1234
  • Bananas1234
times it by y?
JoannaBlackwelder
  • JoannaBlackwelder
Close. That would give us:|dw:1433440631552:dw|
JoannaBlackwelder
  • JoannaBlackwelder
So the numbers of y's still aren't quite the same.
Bananas1234
  • Bananas1234
they arent?
Bananas1234
  • Bananas1234
ok whats next
JoannaBlackwelder
  • JoannaBlackwelder
It looks like we have 2 y's on the left, but 3 on the left.
Bananas1234
  • Bananas1234
i see
Bananas1234
  • Bananas1234
you mean 3 on the right?
JoannaBlackwelder
  • JoannaBlackwelder
Yeah, sorry.
Bananas1234
  • Bananas1234
ok
JoannaBlackwelder
  • JoannaBlackwelder
So, we need one more y on the left.
Bananas1234
  • Bananas1234
ok, so do we mulitply again?
JoannaBlackwelder
  • JoannaBlackwelder
Yep
Bananas1234
  • Bananas1234
|dw:1433440911998:dw|
JoannaBlackwelder
  • JoannaBlackwelder
Yep, great! So, are the denominators the same now?
Bananas1234
  • Bananas1234
yes
JoannaBlackwelder
  • JoannaBlackwelder
Great! So, in the full problem, how do we make that both denominators?
Bananas1234
  • Bananas1234
|dw:1433441111648:dw|
Bananas1234
  • Bananas1234
Like that?
JoannaBlackwelder
  • JoannaBlackwelder
But we can't just change the denominators. We have to also change the numerators to keep everything balanced.
Bananas1234
  • Bananas1234
oh, i forgot about that
Bananas1234
  • Bananas1234
ow do we do that?
Bananas1234
  • Bananas1234
how*
JoannaBlackwelder
  • JoannaBlackwelder
What do we need to multiply by the first denominator to get it to be our LCM?
JoannaBlackwelder
  • JoannaBlackwelder
*LCD
Bananas1234
  • Bananas1234
not sure, sorry.
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433441688086:dw|
Bananas1234
  • Bananas1234
what do i put in the (?)?
Bananas1234
  • Bananas1234
@JoannaBlackwelder
JoannaBlackwelder
  • JoannaBlackwelder
What did we multiply by to get the LCD of the left side?
Bananas1234
  • Bananas1234
by y?
JoannaBlackwelder
  • JoannaBlackwelder
Was that all?
Bananas1234
  • Bananas1234
i think so....
JoannaBlackwelder
  • JoannaBlackwelder
No, |dw:1433442752287:dw| so we need to multiply the left fraction on top and bottom by 2y^2
Bananas1234
  • Bananas1234
oh
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433442908806:dw|
JoannaBlackwelder
  • JoannaBlackwelder
Can you simplify?
Bananas1234
  • Bananas1234
how do i simplify??
JoannaBlackwelder
  • JoannaBlackwelder
Multiply
Bananas1234
  • Bananas1234
multiply the 5 by the 2y^2?
JoannaBlackwelder
  • JoannaBlackwelder
Yep
Bananas1234
  • Bananas1234
10y^2/6x^2y^3?
JoannaBlackwelder
  • JoannaBlackwelder
Yep, great! How about the other fraction?
Bananas1234
  • Bananas1234
|dw:1433443839427:dw| Like this??
Bananas1234
  • Bananas1234
so 8y2/12xy^5?
Bananas1234
  • Bananas1234
8y^2/12xy^5 @JoannaBlackwelder
Bananas1234
  • Bananas1234
is that all i need to do? @JoannaBlackwelder
Bananas1234
  • Bananas1234
please reply i have 20 mins to get this done :( @JoannaBlackwelder
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
  • Bananas1234
ok
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433445935170:dw|
JoannaBlackwelder
  • JoannaBlackwelder
We need to multiply the right fraction by x to make common denominators.
Bananas1234
  • Bananas1234
i got that part
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433446083616:dw|
Bananas1234
  • Bananas1234
i see
JoannaBlackwelder
  • JoannaBlackwelder
:-)
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433446145225:dw|
JoannaBlackwelder
  • JoannaBlackwelder
So, now we can subtract the numerators, and the denominators stay the same.
JoannaBlackwelder
  • JoannaBlackwelder
So, what does that give us?
Bananas1234
  • Bananas1234
6y^2x?
JoannaBlackwelder
  • JoannaBlackwelder
No, I mean for the whole fraction.
Bananas1234
  • Bananas1234
im having a hard time subtracting the bottom
JoannaBlackwelder
  • JoannaBlackwelder
It stays the same. Doesn't subtract.
Bananas1234
  • Bananas1234
ohh i see
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433446648437:dw|
Bananas1234
  • Bananas1234
so,6y^2x/6x^2y^3
JoannaBlackwelder
  • JoannaBlackwelder
No, only like terms can add.
Bananas1234
  • Bananas1234
ok
Bananas1234
  • Bananas1234
so its 10y^2 - 4x/6x^2y^3 is that all??
JoannaBlackwelder
  • JoannaBlackwelder
Well, we can simplify a bit by factoring out a 2
Bananas1234
  • Bananas1234
what 2?
Bananas1234
  • Bananas1234
i do have to get this turned in now, if i don't i will get a 0
Bananas1234
  • Bananas1234
the 2 on 6 and 10??
JoannaBlackwelder
  • JoannaBlackwelder
Yes, and the 4
JoannaBlackwelder
  • JoannaBlackwelder
You can turn it in like that. You should get partial credit
Bananas1234
  • Bananas1234
ok, but if i were to do it some other time what can i do?
JoannaBlackwelder
  • JoannaBlackwelder
|dw:1433447702331:dw|
Bananas1234
  • Bananas1234
ok, thank you for all of your help, sorry that took so long.
JoannaBlackwelder
  • JoannaBlackwelder
And the twos cancel out. |dw:1433447840612:dw|
JoannaBlackwelder
  • JoannaBlackwelder
You're welcome :-)

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