SOLUTION: How do I express as a single fraction in its simplest form: 1 1 ----- - ----- 2x +3 4xsquared - 9

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: How do I express as a single fraction in its simplest form: 1 1 ----- - ----- 2x +3 4xsquared - 9      Log On


   

Question 624091: How do I express as a single fraction in its simplest form:

1 1
----- - -----
2x +3 4xsquared - 9
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
express as a single fraction in its simplest form:
1 1
----- - -----
2x +3 4xsquared - 9
assume the problem is:
1%2F%28%282x%2B3%29%29 - 1%2F%28%284x%5E2-9%29%29
note that the 2nd denominator is the "difference of squares which we can factor"
1%2F%28%282x%2B3%29%29 - 1%2F%28%282x%2B3%29%282x-3%29%29
you can see the common denominator will be (2x+3)(2x-3), so we have
%28%282x-3%29-1%29%2F%28%282x-3%29%282x%2B3%29%29 = %28%282x-4%29%29%2F%28%282x-3%29%282x%2B3%29%29 = %282%28x-2%29%29%2F%28%282x-3%29%282x%2B3%29%29 or %282%28x-2%29%29%2F%28%284x%5E2-9%29%29