SOLUTION: (x+9/x^2-9)-(2/x-3) It has been 4 years since I graduated highschool and I'm having trouble remembering how to do this.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: (x+9/x^2-9)-(2/x-3) It has been 4 years since I graduated highschool and I'm having trouble remembering how to do this.      Log On


   

Question 148489: (x+9/x^2-9)-(2/x-3)
It has been 4 years since I graduated highschool and I'm having trouble remembering how to do this.
Found 2 solutions by mangopeeler07, jim_thompson5910:
Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
It's okay, I will help you.

First start with this
%28x%2B9%29%2F%28x%5E2-9%29-%282%2F%28x-3%29%29

Then factor everything you can possibly factor without going into crazy pointless decimals. in other words, factor x%5E2-9:

%28x%2B9%29%2F%28x-3%29%28x%2B3%29-%282%2F%28x-3%29%29

Multiply 2%2F%28x-3%29 by %28x%2B3%29%2F%28x%2B3%29

%28x%2B9%29%2F%28x-3%29%28x%2B3%29-%282%28x%2B3%29%2F%28x-3%29%28x%2B3%29%29

Simplify 2(x+3)

%28x%2B9%29%2F%28x-3%29%28x%2B3%29-%28%282x%2B6%29%2F%28x-3%29%28x%2B3%29%29

Now do the subtraction

%28x%2B9-2x-6%29%2F%28x-3%29%28x%2B3%29

Simplify the numerator

%28-x%2B3%29%2F%28x-3%29%28x%2B3%29

Take out a negative one in the numerator

%28-1%29%28x-3%29%2F%28x-3%29%28x%2B3%29

Cancel out like terms

%28-1%29%2F%28x%2B3%29

Did it all come back to you?



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29 Start with the given expression.


%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282%29%2F%28x-3%29 Factor x%5E2-9 to get %28x%2B3%29%28x-3%29 (use the difference of squares)


In order to add or subtract any fractions, we need to have every denominator to be the same. So we need to have every denominator equal to the LCD. In this case, the LCD is %28x%2B3%29%28x-3%29


Multiply the second fraction by %28x%2B3%29%2F%28x%2B3%29. Doing this will make the second fraction have a denominator equal to the LCD.


%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%29 Combine the fractions


%28x%2B9%29%2F%28%28x%2B3%29%28x-3%29%29-%282x%2B6%29%2F%28%28x%2B3%29%28x-3%29%29 Distribute



Now that we have equal denominators, we can combine the fractions


%28x%2B9-%282x%2B6%29%29%2F%28%28x%2B3%29%28x-3%29%29 Combine the numerators over the common denominator.


%28x%2B9-2x-6%29%2F%28%28x%2B3%29%28x-3%29%29 Distribute


%28-x%2B3%29%2F%28%28x%2B3%29%28x-3%29%29 Combine like terms.


%28-%28x-3%29%29%2F%28%28x%2B3%29%28x-3%29%29 Factor a -1 from the numerator.


%28-highlight%28%28x-3%29%29%29%2F%28%28x%2B3%29highlight%28%28x-3%29%29%29 Highlight the common terms.



%28-cross%28%28x-3%29%29%29%2F%28%28x%2B3%29cross%28%28x-3%29%29%29 Cancel out the common terms.


%28-1%29%2F%28x%2B3%29 Simplify


So %28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29 simplifies to %28-1%29%2F%28x%2B3%29.


In other words, %28x%2B9%29%2F%28x%5E2-9%29-%282%29%2F%28x-3%29=%28-1%29%2F%28x%2B3%29 where x%3C%3E-3 or x%3C%3E3