## Singlemom76 one year ago Hey everyone back to school can someone help with this problem (x+2)^-1/2 (2x+4)+(x+2)^3/2

1. alffer1

Are you supposed to simplify the problem?

2. Singlemom76

Yes

3. alffer1

ok look at the parentheses on the left. Can you pull out any common factors?

4. alffer1

oh oops I mean one in the middle.

5. Singlemom76

ok but what do I do with those darn exponents. LOL

6. alffer1

just a sec, I'm working it out. will explain as soon as I'm done.

7. alffer1

ok here goes: Pulling out the common 2, you get: 2(x+2)(x+2)^-1/2 + (x+2)^3/2 right?

8. Singlemom76

ok

9. alffer1

So now can you see any terms that can be pulled out of the addition?

10. alffer1

actually first: can you simplify the left side of the addition at all?

11. Singlemom76

the (x+2)^-1/2 goes to the bottom and the 2 can be factored from the (2x+4) leaving 2(x+2) over (x+2)^1/2

12. alffer1

notice that both have a base of (x+2). What does that mean about the exponents?

13. Singlemom76

yea I'm sorry not a clue. Ugh Christmas break ruined me

14. alffer1

When the bases are equal, 2 multiplied exponents can be added. for example: 2^2 * 2^3 = 2^5. In this case, the base is (x+2) and the exponents are 1 and -1/2. soo.....

15. Singlemom76

I am so sorry and feel like an idiot right now. I get that the exponents are multiplied

16. alffer1

exponents should be added. In this case 1-1/2 = 1/2. As a result: you get 2(x+2)^1/2 + (x+2)^3/2 right?

17. Singlemom76

ok oops thats what I meant. But didn't the (-) exponent go to the denominator

18. alffer1

you can do that too, but in this case it's simply easier to add up the exponents, eliminating the denominator altogether.

19. Singlemom76

ok then what do I do?

20. alffer1

Now you have a common term of (x+2)^1/2 that you can pull out of both terms in the addition. It's like the opposite of the distributive property.

21. alffer1

Doing that, you get (x+2)^1/2 times(2 + x + 2), which simplifies to (x+4)(x+2)^1/2. and you're done.

22. Singlemom76

so my final answer should be (x+2)^1/2 + (x+4)

23. alffer1

yup! :)

24. alffer1

oh wait no. They're multiplied, not added.

25. Singlemom76

ok thanks (feel like an idiot) lol

26. alffer1

no problem!