# Thread: "rationalize the denominator and simplify"

1. ## "rationalize the denominator and simplify"

i need help on this question that says rationalize the denominator and simplify.

this is the problem::

+ 1
__________________
-

thank you

2. Originally Posted by needleandthread
i need help on this question that says rationalize the denominator and simplify.

this is the problem::

+ 1
__________________
-

thank you
Multiply by it's conjugate where the conjugate is the same numbers with the opposite sign between them:

$\frac{\sqrt3 +1}{\sqrt{3}+\sqrt{2}}$

The conjugate is $\sqrt{3}-\sqrt{2}$

$\frac{\sqrt3 +1}{\sqrt{3}+\sqrt{2}} \cdot \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}} = \frac{(\sqrt{3} +1)(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}$

Use the difference of two squares on the denominator

3. Originally Posted by needleandthread
i need help on this question that says rationalize the denominator and simplify.

this is the problem::

+ 1
__________________
-

thank you
multiply by $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}$