## anonymous one year ago Simplify.. need help asap... 8/ab + 6/b and (3t2/(t + 2)) x ((t + 2)/t2) thanks!!

1. jim_thompson5910

The first one is $\Large \frac{8}{ab} + \frac{6}{b}$ right?

2. anonymous

yes.

3. jim_thompson5910

what is the LCD in this case?

4. anonymous

i don't know.

5. jim_thompson5910

we have ab as the first denominator and b as the second denominator

6. jim_thompson5910

do you see how the LCD would be ab?

7. anonymous

no.

8. anonymous

:( I'm really bad at math. I'm sorry..

9. jim_thompson5910

maybe replace a and b with numbers

10. jim_thompson5910

say a = 2 b = 3

11. anonymous

okay.

12. jim_thompson5910

ab = 2*3 = 6

13. anonymous

i understand that.

14. jim_thompson5910

if we had 1/6 + 1/3, what would the LCD be?

15. anonymous

6

16. jim_thompson5910

yes because we can multiply the denominator 3 by 2 to get 6

17. jim_thompson5910

we can multiply top and bottom of 1/3 by 2 to get 2/6 1/6 + 1/3 turns into 1/6 + 2/6

18. jim_thompson5910

from there you add straight across and leave the denominator alone

19. anonymous

mhm.

20. jim_thompson5910

the same idea applies here we multiply top and bottom of the second fraction by 'a' $\Large \frac{8}{ab} + \frac{6}{b}$ $\Large \frac{8}{ab} + \frac{6{\color{red}{a}}}{b{\color{red}{a}}}$ $\Large \frac{8}{ab} + \frac{6a}{ab}$

21. jim_thompson5910

then you add the numerators and place that over the denominator

22. anonymous

okat.

23. anonymous

now I'm lost.

24. jim_thompson5910

where at?

25. anonymous

how do we find the answer? or did we already find it and i was lost before then? i thought I've been following.

26. jim_thompson5910

do you see why I multiplied top and bottom of the second fraction by 'a'?

27. jim_thompson5910

I wanted to get every denominator equal to the LCD 'ab'

28. anonymous

okay

29. jim_thompson5910

there's one more step to go

30. anonymous

alright.

31. jim_thompson5910

What does $\Large \frac{8}{ab} + \frac{6a}{ab}$ simplify to?

32. anonymous

8/ab + 6/ab

33. anonymous

i really am lost.

34. anonymous

8/ab+6/b

35. jim_thompson5910

just add up the numerators $\Large \frac{8}{ab} + \frac{6a}{ab}=\frac{8+6a}{ab}$ this is possible because the denominators are both equal to ab

36. anonymous

okay. now how would we do the second one?

37. jim_thompson5910

The second one is $\Large \left(\frac{3t^2}{t+2}\right)\times\left(\frac{t+2}{t^2}\right)$ right?

38. anonymous

t+2 on the sec on one are in a parenthesis.

39. anonymous

and in the first one. its like parenthesis insides of themselves.

40. jim_thompson5910

ok so this? $\Large \left(\frac{3t^2}{(t+2)}\right)\times\left(\frac{(t+2)}{t^2}\right)$

41. anonymous

yes that is correct.

42. jim_thompson5910

first notice this cancellation $\Large \left(\frac{3{\color{red}{\cancel{\color{black}{t^2}}}}}{t+2}\right)\times\left(\frac{t+2}{{\color{red}{\cancel{\color{black}{t^2}}}}}\right)$ the t^2 terms will go away leaving just $\Large \left(\frac{3}{(t+2)}\right)\times\left(\frac{(t+2)}{1}\right)$

43. anonymous

ok what is the next step

44. jim_thompson5910

then the (t+2) terms also cancel $\Large \left(\frac{3}{{\color{red}{\cancel{\color{black}{(t+2)}}}}}\right)\times\left(\frac{{\color{red}{\cancel{\color{black}{(t+2)}}}}}{1}\right)$

45. jim_thompson5910

I'm sure you see how to finish

46. anonymous

so its 3?

47. jim_thompson5910

yep

48. anonymous

thats the easiest thing I've ever seen