SOLUTION: Here is the problem. I have been at it for an hour and still can't seem to figure it out. Can someone out there help me? [3/x-5]-1 / 1-[4/x-5]

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Here is the problem. I have been at it for an hour and still can't seem to figure it out. Can someone out there help me? [3/x-5]-1 / 1-[4/x-5]      Log On


   

Question 78990: Here is the problem. I have been at it for an hour and still can't seem to figure it out. Can someone out there help me?
[3/x-5]-1 / 1-[4/x-5]
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Does your problem look like this?

%28%283%2F%28x-5%29%29-1%29%2F%281-%284%2F%28x-5%29%29%29
In order to subtract fractions we need them to have a common denominator. So lets multiply both 1's by %28x-5%29%2F%28x-5%29

So now we get this after multiplying



Now we can combine the fractions

%28%283-%28x-5%29%29%2F%28x-5%29%29%2F%28%28%28x-5%29-4%29%2F%28x-5%29%29


Distribute the negative

%28%283-x%2B5%29%2F%28x-5%29%29%2F%28%28x-5-4%29%2F%28x-5%29%29

Now combine like terms

%28%28%288-x%29%29%2F%28x-5%29%29%2F%28%28x-9%29%2F%28x-5%29%29

Now when we divide fractions, we multiply the first fraction, by the reciprocal of the 2nd

%28%28%288-x%29%29%2F%28x-5%29%29%2A%28%28x-5%29%2F%28x-9%29%29

Cancel like terms

%28%28%288-x%29%29%2Fcross%28%28x-5%29%29%29%2A%28cross%28%28x-5%29%29%2F%28x-9%29%29
So our expression reduces to

%288-x%29%2F%28x-9%29