need help with simplifying by rationalizing the denominator.

Question

owlfred · Answer

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

anonymous · Answer

when you have:

$$\frac{a}{b-\sqrt{c}}$$

multiply the top and bottom by the conjugate: b+sqrt(c)

$$\frac{a(b+\sqrt{c})}{(b-\sqrt{c})(b+\sqrt{c})}=\frac{ab+a \sqrt{c}}{b^{2}-c}$$

anonymous · Answer

now the denominator is rational

anonymous · Answer

Rationalizing the denominator requires that you multiply above and below by the contents of the denominator. So in this case, you need to multiply above and below by $$b-\sqrt{c}$$
This will give you a new result of $$a(b-\sqrt{c})/b-\sqrt{c})^2$$

anonymous · Answer

(b-sqrt(c))^2=b^2-2bsqrt(c)+c, this is not rational.  you need to multiply by the conjugate to get rid of the radical