## SmokeysTheName Simplify the rational expression. State any restrictions on the variable one year ago one year ago

1. SmokeysTheName

2. SmokeysTheName

3. UnkleRhaukus

can you factorise the numerator and the denominator ?

4. SmokeysTheName

yeah gimme a sec lemme do that real quick

5. SmokeysTheName

the numerator is (t+6)(t-4) im not sure how to factor the denominator.. i always forget.. i think its (t+6)(t-6) -- am i right?

6. UnkleRhaukus

good work, that is right . now you can cancel the common factor

7. SmokeysTheName

you're left with t-4/t-6 right? :D

8. UnkleRhaukus

YES!

9. AravindG

well done @SmokeysTheName :D

10. SmokeysTheName

thank you (: now what do i do?

11. UnkleRhaukus

the restricted value for the variable \(t\) is the value that would make the denominator zero. this values is restricted because you can't divide by zero

12. SmokeysTheName

alright.. so do i have to put t+6 and t-6 equal to zero?

13. UnkleRhaukus

um, just the denominator ( the bottom bit of the fraction )

14. SmokeysTheName

yeah thats what i was talking about lol. okay so the restrictions would be -6 and +6 right?

15. UnkleRhaukus

after you have simplified , not before

16. SmokeysTheName

oh so just +6?

17. UnkleRhaukus

That's right \[\checkmark\]

18. SmokeysTheName

thank you!! (: that helps me a lot. do you mind helping me with a different question i am stuck on?

19. UnkleRhaukus

we can write this as \(t≠6\) , or we could say that \(t\) is defined on the domain \[(-∞,6)\cup(6,∞)\]

20. SmokeysTheName

oh that looks confusing.. (the second part)

21. UnkleRhaukus

if you haven't learnt that notation yet , just say that \(t≠6\) is the restriction they mean the same thing.

22. SmokeysTheName

oh okay. thank you (: can you help me on another question?

23. UnkleRhaukus

um Yes.

24. SmokeysTheName

Find the least common multiple of y^2 – 2y – 15 and y^2 – 7y + 10. how do i do this? im not sure how to do lcm

25. UnkleRhaukus

factorise those expressions,

26. SmokeysTheName

ok one sec.

27. SmokeysTheName

okay for the first equation i got (x-5)(x+3) and for the second equation i got (x-5)(x-2) . is that right? Or no..

28. UnkleRhaukus

you are good at factorising .that is right

29. SmokeysTheName

awh thank you (: in these types of problems i never know where to start. just like the other problem... anyways, is the least common multiple like x-5? or is that wrong ? i always get confused with lcm

30. UnkleRhaukus

now lets consider a simpler example say we were looking for the lcm of 6 and 4 we would factorise 6=2x3 & 4=2x2 the lcm is the product of the non-common factors so 2x3x2 (one of the twos is common) which equals 12

31. UnkleRhaukus

so to find the lcm of (x-5)(x+3) & (x-5)(x-2) multiple the factors ( and dont repeat common factors )

32. SmokeysTheName

ohh ok . so with my problem it would be (x-5)(x+3)(x-2) right? :D

33. UnkleRhaukus

YES!!!

34. SmokeysTheName

:D that makes me excited. i cant thank you enough !(:

35. UnkleRhaukus

you've be great to work with smokey .

36. SmokeysTheName

thank you, you too! (: if i need anymore help i can ask you right?

37. UnkleRhaukus

well i have to sleep kinda soon , but next time you can link me to a question like this @UnkleRhaukus

38. SmokeysTheName

okk. (: i will most definitely do that! thank you again (:

39. AravindG

@SmokeysTheName as UnkleRhaukus told ,you are great to work with I felt the same in our previous questions :) happy to have users like you in OS .Happy openstudying!

40. SmokeysTheName

awwwwh thank you so much ! (: <3

41. AravindG

yw :)