Simplifying fractions with radicals

Question

In Algebra 2, I am given the following problem:

 

√(7) - 5/2√(7) + 3

 

√(7) - 5 is on the top of the fraction, and 2√(7) + 3 is on the bottom. I am told to simplify.

Answer 1

(√(7) - 5) / (2√(7) + 3)
 
 
Multiply the expression by  (2√(7) - 3) / (2√(7) - 3).  This is called rationalizing the denominator.
 
 
(√(7) - 5)(2√(7) - 3) / (2√(7) + 3)(2√(7) - 3) =
 
(14 - 3√(7) - 10√(7) + 15) / (28 - 9) =
 
(-13√(7) + 29) / 19