simplifying fractions with radicals

Question

In Algebra 2, I am given the following equation:

 

√(7) - 5/2√(7) + 3

 

√(7) - 5 is the top of the fraction, and 2√(7) + 3 is the bottom.

 

I am told to simplify. How do I solve this?

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) =

 

(14 - 13√(7) + 15) / 19 =