## anonymous 5 years ago [y^2-2y/y^2+7y-18] X [y^2-81/y^2-11y+18] Simplify the rational expression.

1. anonymous

break the denominators off into factored squares, and cancel terms to simplify.

2. anonymous

i did that and got y(y-9)/(x-2) (y+2)

3. anonymous

4. anonymous

$\frac{y(y - 2)}{(y+9)(y-2)} * \frac{(y+9)(y-9)}{(y+9)(y+2)}$

5. anonymous

oh wait a sec.....on the bottom right i put (y-2) (y+2) for some reason. the rest i got right though.

6. anonymous

hold on let me try this to see if i get it right

7. anonymous

Leaves $\frac{y(y+9)}{(y+9)(y+2)} = \frac{y(y-9)}{(y+9)(y+2)}$

8. anonymous

Ok

9. anonymous

polpak is riqht but i think u still have to cancel the terms

10. anonymous

he did

11. anonymous

ohhh yeah he did... i didnt see the equals siqn... sorry! :))

12. anonymous

[y^2-2y/y^2+7y-18] factor you get [y(y-2)/(y-2)(y+9)]cancel you get y/(y+9) [y^2-81/y^2-11y+18] factor you get [(y+9)(y-9)]/[(y-2)(y-9)] cancel you get (y+9)/(y-2) now you can time; [y/(y+9)]*[(y+9)/(y-2)] [y^2+9y)]*[(y^2+7y-14)] from here can you do your own?

13. anonymous

would you get rid of y-2??? cuz thats the only way im getting the y(y+9)

14. anonymous

you foil

15. anonymous

time

16. anonymous

[y/(y+9)]*[(y+9)/(y-2)] sorry time not divi [y/(y+9)]*[(y+9)*(y-2)]

17. anonymous

Whoops, was that a -11 in the denominator of the second fraction?

18. anonymous

My font makes it hard to read those sometimes. Lets try this again.

19. anonymous

okay :D ha.

20. anonymous

srry I wrong again,it hard to tye ,easy for me to write

21. anonymous

$\frac{y^2-2y}{y^2+7y-18} \times \frac{y^2-81}{y^2-11y+18}$ $= \frac{y(y-2)}{(y+9)(y-2)} \times \frac{(y+9)(y-9)}{(y-9)(y-2)}$ $= \frac{y}{(y+9)} \times \frac{(y+9)}{(y-2)}$ $= \frac{y(y+9)}{(y+9)(y-2)}$ $= \frac{y}{y-2}$

22. anonymous

[y^2+9y)]*[(y^2+7y-14)]not this [y^2+9y)]*[(y^2+7y-18)] this correct

23. anonymous

While that's correct, yours can be simplified further Nancy.

24. anonymous

Well correct assuming that by * you mean / that is.

25. anonymous

ha okay thanks polpak and nancy i really appreciate your help!

26. anonymous

Did you follow all that Carr?

27. anonymous

The best strategy to use with these is to leave them factored as long as possible so you can quickly see what cancels.

28. anonymous

yeah i got a little head of my self and put the wrong number but thank you both!

29. anonymous

That's ok, I misread a negative so we all make mistakes ;)

30. anonymous

yes still time (y/y-2)*(y+9)(y-2)*[y^2-81/y^2-11y+18]

31. anonymous

from here are you OK to do your own? [y^2+9y)]*[(y^2+7y-18)]

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