Bananas1234 one year ago Simplify. u^2-4/u^2 - 2u

1. nikato

2. anonymous

you can factorize u^2-4 to (u-2)(u+2) and next exp as u(u-2) cancel out (u-2) from denom and num

3. Bananas1234

u + 2, u is not 2?

4. UsukiDoll

we have a perfect square on the numerator... can we split that up in the form of (a+b)(a-b) where a = x and b =2?!

5. Bananas1234

i dont think so, can we?

6. UsukiDoll

whatttttttttttttttttttt! pop quiz what the square root of 4

7. Bananas1234

2

8. UsukiDoll

yes... whenever we have a perfect square we can split (a^2-b^2) in the form of (a+b)(a-b)

9. UsukiDoll

so since a = x and b = 2 what is the numerator... we can split it up in the form of (a+b)(a-b)

10. UsukiDoll

a = x =u b = 2

11. Bananas1234

i see

12. Bananas1234

so what do i do next

13. UsukiDoll

what do you have for the numerator first?

14. Bananas1234

u + 2?

15. UsukiDoll

no you're missing something I'll give an example (x^2-9) =(x+3)(x-3) now follow that pattern with u^2-4

16. UsukiDoll

it's 3 on the example because the square root of 9 is 3

17. Bananas1234

i am not sure i am following you

18. UsukiDoll

(u^2-4) the term u^2 is a perfect square and the same goes for 4 so the square root of u^2 is u and the square root of 4 is 2 whenever we have something like u^2 - 4 , it is a perfect square polynomial in the form of (u^2-4) = (u+2)(u-2)

19. Bananas1234

ok

20. UsukiDoll

now for the denominator u^2 can also be written as uu... eventually you may be required to be swift in factoring and taking out like terms u^2-2u I can take a u out and it becomes u(u-2) to see it easier uu-2u and since we have a u on the left and u on the right we can take that out

21. Bananas1234

ok

22. UsukiDoll

so now we have (u+2)(u-2) / u(u-2) so what does the numerator and denoiminator have in common that we can remove.

23. Bananas1234

u-2

24. UsukiDoll

yes! so we have (u+2)/(u)

25. Bananas1234

i think i understand better now

26. UsukiDoll

hmm if we have to simplify further we can split (u+2)/(u) into 2 fractions because they have the same denominator u/u +2/u 1+ 2/u or we can leave the answer like that

27. Bananas1234

based on my options i think its ok to leave it

28. UsukiDoll

yeah that's fine ^^

29. Bananas1234

so is it u +2/u, u is not 0 or u +2/u, u is not 2, u is not 0 ? and how do i find out?

30. Bananas1234

@UsukiDoll

31. UsukiDoll

the denominator of u is the whole entire thing $\frac{u+2}{u}$

32. UsukiDoll

since they share a single denominator we can split it up into 2 different fractions or leave it as is.

33. UsukiDoll

$\frac{u}{u} +\frac{2}{u} \rightarrow 1 + \frac{2}{u}$

34. UsukiDoll

we can't have u = 0 .. because anything divided by 0 is undefined.

35. Bananas1234

i see

36. Bananas1234

Thanks