# Thread: [SOLVED] Help! - Simplification

1. ## [SOLVED] Help! - Simplification

Hello!

I would really appreciate some help, I need to simplify these;

x + √x
------- (I know that this one is √x, but how does it get to that?)
1 + √x

and;

x
------- + √(1-x)
√(1-x)

and;

1 - x
-------
1 + √x

Thank you!

2. Originally Posted by weasley74
Hello!

I would really appreciate some help, I need to simplify these;

x + √x
------- (I know that this one is √x, but how does it get to that?)
1 + √x
factor out $\displaystyle \sqrt{x}$ from the numerator:

we get: $\displaystyle \frac {\sqrt{x} (\sqrt{x} + 1)}{1 + \sqrt{x}}$

now continue

and;

x
------- + √(1-x)
√(1-x)
begin by combining the fractions. then what would you get?

and;
1 - x
-------
1 + √x
Thank you!
think of $\displaystyle 1 - x$ as $\displaystyle 1^2 - (\sqrt{x})^2$

now expand that using the difference of two squares. what do you get?

3. Thank you - for not really telling me the answers but instead giving me just enough hints to work it out for myself. ;D

Thanks again.

4. Originally Posted by weasley74
Thank you - for not really telling me the answers but instead giving me just enough hints to work it out for myself. ;D

Thanks again.
you're very much welcome