## anonymous 5 years ago need help with simplifying by rationalizing the denominator.

1. Owlfred

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2. anonymous

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

3. anonymous

now the denominator is rational

4. anonymous

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 $a(b-\sqrt{c})/b-\sqrt{c})^2$

5. anonymous

(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