Question 169758
Rationalize each denominator Adn please show me how u work it out..Thank You 
sqrt7 + 3/ sqrt7 - 3
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{{{(sqrt(7) + 3)/(sqrt(7) - 3)}}}  I think this is what you meant.
The object is to get rid of the radical in the DEN.
To do that, multiply NUM and DEN by the "conjugate."  That term applies to complex numbers, I'm not sure it's the one for this problem, but the approach is similar.
The "conjugate" of (sqrt(7) - 3) is (sqrt(7) + 3), a change of sign.
{{{(sqrt(7) + 3)/(sqrt(7) - 3)}}}
= {{{(sqrt(7) + 3)*(sqrt(7) + 3)/((sqrt(7) - 3)*(sqrt(7) +3))}}}
= {{{(sqrt(7) + 3)*(sqrt(7) + 3)/(7 - 9)}}}
= {{{(7 + 6sqrt(7) + 9)/(-2)}}}
= {{{-8 - 3sqrt(7)}}}
PS  I looked it up, conjugate is the correct term.