## Spartan_Of_Ares 2 years ago can i get help with rational expression

1. Spartan_Of_Ares

here it is

2. mathstudent55

You mean a rational expression.

3. mathstudent55

A simplified rational fraction can't have radicals in the denominator.

4. mathstudent55

|dw:1356657899257:dw|

5. Spartan_Of_Ares

cross multiplication?

6. mathstudent55

Now you need to look at all prime factors of 98 and twelve.

7. mathstudent55

No, we're just simplifying, one step at a time.

8. mathstudent55

What are the prime factors of 98 and of 12?

9. Spartan_Of_Ares

7 7 2 and 3 2 2

10. mathstudent55

Great. Every two of the same factor can be taken out of the root.

11. Spartan_Of_Ares

so 7 2 and 3 2

12. mathstudent55

|dw:1356658078286:dw|

13. mathstudent55

|dw:1356658116825:dw|

14. mathstudent55

As you mentioned, the 7 came out in the numerator, and the 2 came out in the denominator. But we still have a radical in the denominator which we can't leave there.

15. Spartan_Of_Ares

what would i do to remove it?

16. mathstudent55

|dw:1356658236596:dw|

17. mathstudent55

We are going to use both of the above ideas to remove the radical from the denominator. First look at the denominator. What do you need to multiply the radical of the denominator to get rid of the radical? See example 1 above in drawing.

18. Spartan_Of_Ares

@mathstudent55 times it self?

19. mathstudent55

Right. If you multiply sqrt(3) by sqrt(3), you get sqrt(9) = 3, so you don't have a radical any more.

20. Spartan_Of_Ares

so my denominator would be 18?

21. mathstudent55

Now you need to look at example 2. in the drawing. If you multiply the denominator of the fraction by sqrt(3) what must you do to the numerator?

22. Spartan_Of_Ares

multiply by the same

23. mathstudent55

Exactly. So now look at the next drawing:

24. mathstudent55

|dw:1356658755142:dw|

25. mathstudent55

sqrt(9) is simply a whole number. That was the whole purpose of multiplying the denominator by sqrt(3)

26. Spartan_Of_Ares

wait what do you mean do i just get\[18\] as my denominator?

27. mathstudent55

You have 2 * sqrt(9) in the denominator. What is sqrt(9)?

28. Spartan_Of_Ares

3

29. mathstudent55

Right. So now you have this: |dw:1356658960784:dw|

30. mathstudent55

One more step.

31. Spartan_Of_Ares

6 is the denominator

32. mathstudent55

Correct!

33. mathstudent55

|dw:1356659058827:dw|

34. mathstudent55

This is considered simplified.

35. Spartan_Of_Ares

thank you for the help

36. mathstudent55

You're welcome.