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The idea is to get rid of the square root in the denominator. For this purpose, you must multiply numerator and denominator by the square root of 6 in this case.
Determine the lowest common denominator. Multiply the numerator and denominator of each fraction by a number that will result in the denominator becoming the LCD. The purpose for multiplying both the numerator and denominator is that any number divided by itself = 1, and when you multiply something by 1, you don't change it. When subtracting two fractions with the same denominators, the first numerator minus the second numerator equals the numerator of the result, and the result has the same denominator (the LCD). Simplify.
A Denominator. no problemo...The denominator.
Numerator on top; denominator on the bottom.
Like denominator is the same denominator as the nonzero numbers.