# Thread: I would lkike a problem done and the steps explained (reducing rational expressions)

1. ## I would lkike a problem done and the steps explained (reducing rational expressions)

(18u^6v^5+24u^3v^3)/42u^2v^5

help??!
I don't quite understand how to decide which elements to pull/ factor out etc.
step by step explanation would be lovely!

2. Originally Posted by lindseyb
(18u^6v^5+24u^3v^3)/42u^2v^5

help??!
I don't quite understand how to decide which elements to pull/ factor out etc.
step by step explanation would be lovely!
Numerator:
$\displaystyle 18=6\cdot 3$

$\displaystyle 24=6\cdot 4$

$\displaystyle u^6=u^3\cdot u^3$

$\displaystyle v^5=v^3\cdot v^2$

Denominator:
$\displaystyle 42=6\cdot 7$

What do you think you should factor out?

3. The highest common factor of the numerator is $\displaystyle \displaystyle 6u^3v^3$. After you have factorised the numerator, is there anything that cancels with the denominator?

4. so I pull the 6 out front of them all, then the ^3 in the numerator?
which would make it

6(3u^3v^2)^3 6(4uv)3/ 6(7u^2v^5)?

5. Originally Posted by lindseyb
so I pull the 6 out front of them all, then the ^3 in the numerator?
which would make it

6(3u^3v^2)^3 6(4uv)3/ 6(7u^2v^5)?
$\displaystyle \displaystyle\frac{6u^3v^3(3u^3v^2+4)}{6u^2v^3(7)}$

6. Alrighty! That makes sooo much more sense!
from here can I cancel the 6u^3 to become u?

so the final answer would be

u(3u^3v^2+4v^2)/ v^3(7)

7. Originally Posted by lindseyb
Alrighty! That makes sooo much more sense!
from here can I cancel the 6u^3 to become u?

so the final answer would be

u(3u^3v^2+4v^2)/ v^3(7)

8. oh! Can I combine them??

3v^2+4v^2?

so
u(3u^7v^2)/ v^3(7)

9. Originally Posted by lindseyb
oh! Can I combine them??

3v^2+4v^2?

so
u(3u^7v^2)/ v^3(7)
Originally Posted by dwsmith
$\displaystyle \displaystyle\frac{uv^3(3u^3v^2+4)}{v^3(7)}$

10. AH! I'm sorry, I forgot to rewrite the v^3 in the denominator....
that makes sense
so the final FINAL result is u(3u^3v^2+4)/ 7

11. Originally Posted by lindseyb
AH! I'm sorry, I forgot to rewrite the v^3 in the denominator....
that makes sense
so the final FINAL result is u(3u^3v^2+4)/ 7
Correct.

12. yay!! Thank you!

13. one more??!

if (x^2-4)/(x^2+4)
am I allowed to cancel the x^2's?

14. Originally Posted by lindseyb
one more??!

if (x^2-4)/(x^2+4)
am I allowed to cancel the x^2's?
No.

It doesn't simplify.

15. Alrighty, thank you.

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