\frac{ 5( 3 \color{red}{+} 2\sqrt{6}) }{ (3 - 2\sqrt{6} ) ( 3 \color{red}{+} 2\sqrt{6})} \\ \frac{ 7}{ \sqrt{2} + \sqrt{5}} Keep in mind that some radicals are … Below is some background knowledge that you must remember in order to be able to understand the steps we are going to use. \\ \frac{ 7 \sqrt{2} - 7\sqrt{5} } The way to do rationalizing the denominator is simple. Rationalize the denominator and simplify. radical in the denominator. - [Voiceover] Let's see if we can find the limit as x approaches negative 1 of x plus 1 over the square root of x plus 5 minus 2. \\ \frac{ \sqrt{7} \sqrt{5} -\sqrt{7}\sqrt{7} -\sqrt{5}\sqrt{5} + \sqrt{5}\sqrt{7} } \\ \frac{5 \color{red}{-} 2\sqrt{ 7 } }{5 \color{red}{-} 2\sqrt{ 7 } } \cdot \frac{ \frac{ 6 -3\sqrt{5} } { $$more gifs . \frac{ 3 \sqrt{7} \color{red}{-} 6 } \frac{ 27 - 9\sqrt{5} } \sqrt{2} \color{red}{-} \sqrt{5} Multiplying a fraction by 1 \frac{ 5}{ 3 - 2\sqrt{6} } Step 2: Distribute (or FOIL) both the numerator and the denominator. Remember to find the conjugate all you have to do is change the sign between the two terms. \frac{ 7 \sqrt{2} - 7\sqrt{5} } Interactive simulation the most controversial math riddle ever!$$, $${ \sqrt{5} \sqrt{5} \color{red}{ -\sqrt{5}\sqrt{7}+\sqrt{5}\sqrt{7} }-\sqrt{7}\sqrt{7}} = \frac{3 (2 \color{red}{-} \sqrt{5} )} { (2\color{red}{+} \sqrt{5} )(2\color{red}{-} \sqrt{5} ) }$$, Identify the conjugate of the denominator I could take a 3 out of the denominator of my radical fraction if I had two factors of 3 inside the radical. \cdot $$,$$ \sqrt{7} \color{red}{-} 2 It can rationalize denominators with one or two radicals.  The most common used irrational numbers that are used are radical numbers, for example √3. \frac{ 27 - 9\sqrt{5} } \frac{ -12 + 2 \sqrt{35} } { ( \sqrt{2} + \sqrt{5})( \sqrt{2} \color{red}{-} \sqrt{5})} \frac{ 5}{ \color{red}{ 3 - 2\sqrt{6}} } $$,$$ \\ \color{red}{ 3 + \sqrt{5} } When an expression involving square root radicals is written in simplest form, it will not contain a radical in the denominator. Since this is essentially equal to 1 (that is, it is 1 unless x = 1or x = 0, in which case it is  Rationalization is the process of removing the imaginary numbers from the denominator of an algebraic expression. \\ \frac{ \sqrt{7} -\sqrt{5} }{ \color{red}{ \sqrt{5} + \sqrt{7} }} \cdot more gifs . 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