Rationalize the expression and simplify

[Nazariy]

I have got a bit of trouble interpreting what am I supposed to be doing here.

Part a is to rationalize and simplify :(sqrt(10))/(sqrt(5)-2), this is understandable, I remove the square root in the denominator by multiplying numerator and denominator by sqrt(5)+2. And then I simplify the expression so that it equals: 5sqrt(2)+2sqrt(10).

The next part, part b, is quite confusing for me. I am supposed to rationalize and simplify this expression: (sqrt(4+h)-2)/h
Isn't the above already rational?

Also, sorry for not using LaTex, can't get a grasp of it yet.

Thank you.

 

[pka]

The next part, part b, is quite confusing for me. I am supposed to rationalize and simplify this expression: (sqrt(4+h)-2)/h

\(\displaystyle \dfrac{{\sqrt {4 + h} - 2}}{h} = \dfrac{{(4 + h) - 4}}{{h\left( {\sqrt {4 + h} + 2} \right)}}\)

 

[Nazariy]

\(\displaystyle \dfrac{{\sqrt {4 + h} - 2}}{h} = \dfrac{{(4 + h) - 4}}{{h\left( {\sqrt {4 + h} + 2} \right)}}\)

I understand this, but now we have a square root in denominator, so it's not rationalized, or is it?

 

[pka]

I understand this, but now we have a square root in denominator, so it's not rationalized, or is it?

The point is you are preparing to do difference quotients.
The h in the numerator and denominator will divide off.
As \(\displaystyle h\to 0\) we get \(\displaystyle \dfrac{1}{4}\).

 

[mmm4444bot]

sorry for not using LaTex, can't get a grasp of it yet.

LaTex is not required, on these boards. (I hope that we did not give that impression.)

There are standard conventions, for typing mathematical expressions using only ASCII characters.

Please check out THIS PAGE.

Cheers :cool:

 

[Dale10101]

You might like this.

Also, sorry for not using LaTex, can't get a grasp of it yet.

Thank you.

Here is a post that I wrote and posted in the "Math odds and ends" forum concerning a free online equation editor that will simultaneously produce both a paste-able .gif file of your equation and the corresponding LaTex code. Note that it comes with a warning and it is up to you to decide if learning to use it detracts too much from limited study time ... for some circumstances yes, for others no.

I affirm the post above that states that using the guidelines provided therein allows most posts to be written most quickly and unambiguously using only the keyboard. i.e. don't waste your time with the editor if you have no interest.

"Math odds and ends" "Free online equation editor"

http://www.freemathhelp.com/forum/threads/85832-Free-Online-equation-editor

 

[Nazariy]

LaTex is not required, on these boards. (I hope that we did not give that impression.)

There are standard conventions, for typing mathematical expressions using only ASCII characters.

Please check out THIS PAGE.

Cheers :cool:

Yeap, read that. Thank you.

 

[Nazariy]

Here is a post that I wrote and posted in the "Math odds and ends" forum concerning a free online equation editor that will simultaneously produce both a paste-able .gif file of your equation and the corresponding LaTex code. Note that it comes with a warning and it is up to you to decide if learning to use it detracts too much from limited study time ... for some circumstances yes, for others no.

I affirm the post above that states that using the guidelines provided therein allows most posts to be written most quickly and unambiguously using only the keyboard. i.e. don't waste your time with the editor if you have no interest.

"Math odds and ends" "Free online equation editor"

http://www.freemathhelp.com/forum/threads/85832-Free-Online-equation-editor

Oh yes, I was thinking about the editor perhaps that could do the job for me. Thanks, I will check it out.

 

[Dale10101]

Like your idea:

Oh yes, I was thinking about the editor perhaps that could do the job for me. Thanks, I will check it out.

Like your idea posted elsewhere so am sharing it here.

"Actually a good idea with just posting the .gif. I can actually just use Word Equation creator, print-screen the formula and paste it as a .gif."

Am not sure how the print-screen thing works but I bet it is as simple as just that.

 

[Nazariy]

Like your idea posted elsewhere so am sharing it here.

"Actually a good idea with just posting the .gif. I can actually just use Word Equation creator, print-screen the formula and paste it as a .gif."

Am not sure how the print-screen thing works but I bet it is as simple as just that.

Yeah, works perfectly. Posted a new thread with all the equations!

Basically you have a key on your keyboard that says "Prt Sc". You create equation in word, press that button. Go to Paint, crop the image and save it as .gif, then when you need your equation, insert it here via the "Insert Image" option and its done!

There is an equivalent button in Mac, but can't remember it. Perhaps some other users who have a Mac can share.

 

[Quaid]

TIP: Users of Windoze7 or Windoze8 have the Snipping Tool. This applet effectively combines the PRTSC-MSPAINT-PASTE-CROP steps into a single step. :cool:

 

[Nazariy]

TIP: Users of Windoze7 or Windoze8 have the Snipping Tool. This applet effectively combines the PRTSC-MSPAINT-PASTE-CROP steps into a single step. :cool:

Sweet!! Never realized there is such a thing! Thanks!

 

[Dale10101]

Snipping tool

TIP: Users of Windoze7 or Windoze8 have the Snipping Tool. This applet effectively combines the PRTSC-MSPAINT-PASTE-CROP steps into a single step. :cool:

Didn't know.

The snipping tool can be located by typing "Snipping tool" in the Start search box .... the link

http://windows.microsoft.com/en-us/windows/snipping-tool-faq#1TC=windows-7

... discusses the tool, several save options,

[FONT=WOL_Reg]"When you capture a snip, it is automatically copied to the Clipboard so that you can quickly paste it into a document, e‑mail, or a presentation. You can also save a snip as an HTML, PNG, GIF, or JPEG file. After you capture a snip, you can save it by clicking the [FONT=WOL_Bold]Save Snip[/FONT] button in the mark-up window."[/FONT][FONT=WOL_Reg]


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