SOLUTION: Subtract. Simplify, if possible. 5-w/w-9 - 9w-7/9-w

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Subtract. Simplify, if possible. 5-w/w-9 - 9w-7/9-w      Log On


   

Question 125727: Subtract. Simplify, if possible.
5-w/w-9 - 9w-7/9-w
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%285-w%29%2F%28w-9%29+-+%289w-7%29%2F%289-w%29

In order to perform this addition, you first need to find a common denominator. Notice that -(a-b) = (b-a) for all a and b, so we can rewrite the expression:

%285-w%29%2F%28w-9%29+-+%289w-7%29%2F%28-%28w-9%29%29

And the common denominator becomes -%28w-9%29

%28-%285-w%29%29%2F%28-%28w-9%29%29-%289w-7%29%2F%28-%28w-9%29%29

Now combine the numerators:

%28-%285-w%29-%289w-7%29%29%2F%28-%28w-9%29%29

Distribute and remove parentheses:

%28-5%2Bw-9w%2B7%29%2F%289-w%29

Collect terms:

red%28%282-8w%29%2F%289-w%29%29

You could factor a 2 out of the numerator and make it %282%281-4w%29%29%2F%289-w%29, but there is little value in that. I would just leave it at red%28%282-8w%29%2F%289-w%29%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%285-w%29%2F%28w-9%29-%289w-7%29%2F%289-w%29 Start with the given expression.

%285-w%29%2F%28w-9%29-%28-%289w-7%29%29%2F%28w-9%29 Factor out a negative 1 from 9-w to get -%28w-9%29

%285-w%29%2F%28w-9%29%2B%289w-7%29%2F%28w-9%29 Subtract the negative to add.


%285-w%2B9w-7%29%2F%28w-9%29 Combine the fractions


%288w-2%29%2F%28w-9%29 Combine like terms.



So %285-w%29%2F%28w-9%29-%289w-7%29%2F%289-w%29 simplifies to %288w-2%29%2F%28w-9%29. In other words, %285-w%29%2F%28w-9%29-%289w-7%29%2F%289-w%29=%288w-2%29%2F%28w-9%29