- Thread starter
- #1

#### wishmaster

##### Active member

- Oct 11, 2013

- 211

For example how do you solve this one?

\(\displaystyle \frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}\)

Thank you for replies!

- Thread starter wishmaster
- Start date

- Thread starter
- #1

- Oct 11, 2013

- 211

For example how do you solve this one?

\(\displaystyle \frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}\)

Thank you for replies!

A rule of thumb for fractions is to get a common denominator and to always attempt to rationalise denominators.

For example how do you solve this one?

\(\displaystyle \frac{\frac{1}{2}}{1-\frac{\sqrt{2}}{2}}\)

Thank you for replies!

What have you tried so far?

- Thread starter
- #3

- Oct 11, 2013

- 211

To multiply the fraction with 2.A rule of thumb for fractions is to get a common denominator and to always attempt to rationalise denominators.

What have you tried so far?

- Admin
- #4

I assume you mean to multiply by:To multiply the fraction with 2.

\(\displaystyle 1=\frac{2}{2}\)

This is a good first step. What did you get in doing so?

- Thread starter
- #5

- Oct 11, 2013

- 211

Yes,Mark,i did it so as you said. Actualy i understand this,but i am wondering if there some other way to deal with this.....I assume you mean to multiply by:

\(\displaystyle 1=\frac{2}{2}\)

This is a good first step. What did you get in doing so?

And i got:

\(\displaystyle \frac{1}{2-\sqrt{2}}\)

- Admin
- #6

Okay, now you want to rationalize the denominator. Think of the difference of squares formula...Yes,Mark,i did it so as you said. Actualy i understand this,but i am wondering if there some other way to deal with this.....

And i got:

\(\displaystyle \frac{1}{2-\sqrt{2}}\)

- Thread starter
- #7

- Oct 11, 2013

- 211

I multiply fraction with \(\displaystyle (2+\sqrt{2})\)Okay, now you want to rationalize the denominator. Think of the difference of squares formula...

So i got:

\(\displaystyle \frac{2+\sqrt{2}}{2}\)

- Admin
- #8

Good! You could choose to leave it like that, or express it as:I multiply fraction with \(\displaystyle (2+\sqrt{2})\)

So i got:

\(\displaystyle \frac{2+\sqrt{2}}{2}\)

\(\displaystyle 1+\frac{\sqrt{2}}{2}\)

- Thread starter
- #9

- Oct 11, 2013

- 211

Good! You could choose to leave it like that, or express it as:

\(\displaystyle 1+\frac{\sqrt{2}}{2}\)

thank you!

- Admin
- #10

The new topic is here:

http://mathhelpboards.com/pre-algebra-algebra-2/isolating-radical-7480.html