Help please! Rationalize the numerator
- Thread starter O'Brian
- Start date
skeeter
Elite Member
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- Dec 15, 2005
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\(\displaystyle \L \frac{\sqrt{a} - \sqrt{b}}{a^2 - b^2} \frac{\sqrt{a} + \sqrt{b}}{\sqrt{a} + \sqrt{b}}\)
\(\displaystyle \L \frac{a - b}{(a - b)(a + b)(\sqrt{a} + \sqrt{b})}\)
\(\displaystyle \L \frac{1}{(a+b)(\sqrt{a} + \sqrt{b})}\)
note that the same result can be achieved w/o rationalization ...
\(\displaystyle \L \frac{\sqrt{a} - \sqrt{b}}{a^2 - b^2}\)
\(\displaystyle \L \frac{\sqrt{a} - \sqrt{b}}{(a-b)(a+b)}\)
\(\displaystyle \L \frac{\sqrt{a} - \sqrt{b}}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})(a+b)}\)
\(\displaystyle \L \frac{1}{(\sqrt{a} + \sqrt{b})(a+b)}\)
\(\displaystyle \L \frac{a - b}{(a - b)(a + b)(\sqrt{a} + \sqrt{b})}\)
\(\displaystyle \L \frac{1}{(a+b)(\sqrt{a} + \sqrt{b})}\)
note that the same result can be achieved w/o rationalization ...
\(\displaystyle \L \frac{\sqrt{a} - \sqrt{b}}{a^2 - b^2}\)
\(\displaystyle \L \frac{\sqrt{a} - \sqrt{b}}{(a-b)(a+b)}\)
\(\displaystyle \L \frac{\sqrt{a} - \sqrt{b}}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})(a+b)}\)
\(\displaystyle \L \frac{1}{(\sqrt{a} + \sqrt{b})(a+b)}\)