## Jamierox4ev3r one year ago Math Review Day 3! 6e. Rationalize the expression and simplify.

1. Jamierox4ev3r

Let me re-type the question 6e. Rationalize the expression and simplify $$\huge\frac{\sqrt{4+h}-2}{h}$$

2. anonymous

Is this root just for 4? Or h also?

3. Jamierox4ev3r

the root is $$\sqrt{4+h}$$ @joyraheb

4. Nnesha

i guess multiply the numerator and the denominator by the conjugate of the numerator

5. Jamierox4ev3r

I do believe that the first step would be to multiply the whole expression by the conjugate of the numerator. So I assume that it would look a little like this: $$\huge\frac{\sqrt{4+h}-2}{h}\times\huge\frac{\sqrt{4+h}+2}{\sqrt{4+h}+2}$$

6. Jamierox4ev3r

LOL you read my mind XD There is a lot of multiplying of conjugates in Algebra. A common trend that I recall

7. Jamierox4ev3r

If you multiply these, you should get $$\huge\frac{(4+h)-4}{h(\sqrt{4+h}+2}$$ right?

8. Nnesha

yes right!

9. Jamierox4ev3r

yes! oops wait i think a parentheses is missing in in the denominator $$\huge\frac{(4+h)-4}{h(\sqrt{4+h})+2}$$

10. Jamierox4ev3r

anyhow, from here I'm a little stuck. I know the in the numerator, 4 and -4 cancel out, so you're left with h...but what happens in the denominator?

11. Nnesha

yes right $$\huge\rm \frac{\color{reD}{4}+h\color{reD}{-4}}{h(\sqrt{4+h}+2)}$$$\rm \frac{ h }{ h(\sqrt{4+h}+2)}$ can you cancel out anything ?

12. Jamierox4ev3r

oh wait! i see. So i mentioned canceling out in the numerator, but it seems like something in the numerator and denominator can be cancelled out $$\huge\rm \frac{\color{reD}{4}+\color{green}h\color{reD}{-4}}{\color{green}h(\sqrt{4+h}+2)}$$ The things in green become 1, so wouldn't you have this: $$\huge\frac{1}{\sqrt{4+h}+2}$$

13. Nnesha

parentheses should be aftr 2 cuz it's one expression (sqrt{4+h}+2)

14. Nnesha

that's right!

15. Jamierox4ev3r

oh true, whoops XD and ty ;-;

16. Nnesha

np don't cry:(

17. Jamierox4ev3r

yeah i put the parentheses in the wrong place earlier. my bad hehe I'm fine. From there, am I done?

18. Jamierox4ev3r

19. Nnesha

btw do you have the answer ? just want to know cuz most of times we r not allowed to leave the square root at the denominator

20. Nnesha

yes i think so we can't do anything else with that exprssion

21. Jamierox4ev3r

hmmm lemme check online. The textbook doesn't have the answers in it, but the textbook's website has them. Brb

22. Nnesha

oh cool

23. Jamierox4ev3r

Yep that's it. Thank you thank you! XD

24. Nnesha

my pleasure