ADVANCED EXERCISES-Square Roots and Other Radicals
(4) For the function 
, evaluate the following expression: 
SOLUTION: First let's evaluate the parts of the numberator of this expression.
Of course, . And so, 
. Now we use these in the given expression to obtain:
Now we have a complex fraction to simplify. Let's first focus on simplifying the numerator, by writing the fractions in the numerator with a common denominator (
). (Alternatively, we could multiply numerator and denominator of the "big" fraction by the common denominator of the fractions in the numerator.) So the expression becomes:
In the last step, we used the fact that dividing by ( x - 2 ) in the main fraction is the same as multiplying by its reciprocal, 1 / ( x - 2 ) .
So multiplying the two fractions gives us:
But we can do more with this! Let's rationalize this expression by multiplying numerator and denominator by the conjugate of the numerator (
).
In the fourth line, we wrote ( 2 - x ) as -( x - 2 ) to see the common factor.
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