Question 534443
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(sqrt(a+3))/ (2+3(sqrt(a+3)))  Remove the radical from the denominator by rationalizing the denominator.<P>
Remember that (a+b)(a-b) = a^2 + b^2.  We can remove a sqrt from the denominator a+sqrt  by multiplying by a-sqrt.  We can always multiply an expression by 1 without changing its value.  1 can be written as (a-sqrt)/(a-sqrt)<P>

In this case multiply by (2-3(sqrt(a+3)))/(2-3(sqrt(a+3))).<P>

((sqrt(a+3))/ (2+3(sqrt(a+3)))) * (2-3(sqrt(a+3))) = <P>

(2sqrt(a+3) -3(a+3)) / (4 - 9(a+3))