SOLUTION: Hi. I'm trying to solve 2xy+5x-2y-5 over 3xy+4x-3y-4. Thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi. I'm trying to solve 2xy+5x-2y-5 over 3xy+4x-3y-4. Thank you!      Log On


   

Question 274297: Hi. I'm trying to solve 2xy+5x-2y-5 over 3xy+4x-3y-4. Thank you!
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The key to this problem is factoring


Let's factor 2xy%2B5x-2y-5


2xy%2B5x-2y-5 Start with the given expression.


%282xy%2B5x%29%2B%28-2y-5%29 Group the terms.


x%282y%2B5%29%2B%28-2y-5%29 Factor out the GCF 'x' from the first group.


x%282y%2B5%29-%282y%2B5%29 Factor out the GCF -1 from the second group.


%28x-1%29%282y%2B5%29 Factor out the GCF 3y%2B4 from the entire expression.


So 2xy%2B5x-2y-5 factors to %28x-1%29%282y%2B5%29

--------------------------------

Now let's factor 3xy%2B4x-3y-4


3xy%2B4x-3y-4 Start with the given expression.


%283xy%2B4x%29%2B%28-3y-4%29 Group the terms.


x%283y%2B4%29%2B%28-3y-4%29 Factor out the GCF 'x' from the first group.


x%283y%2B4%29-%283y%2B4%29 Factor out the GCF -1 from the second group.


%28x-1%29%283y%2B4%29 Factor out the GCF 3y%2B4 from the entire expression.


So 3xy%2B4x-3y-4 factors to %28x-1%29%283y%2B4%29

------------------------------------------------


Now that we have the factorizations, we can now simplify:


%282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29 Start with the given expression.


%28%28x-1%29%282y%2B5%29%29%2F%283xy%2B4x-3y-4%29 Factor the numerator (see the first factorization above)


%28%28x-1%29%282y%2B5%29%29%2F%28%28x-1%29%283y%2B4%29%29 Factor the denominator (see the second factorization above)


%28highlight%28%28x-1%29%29%282y%2B5%29%29%2F%28highlight%28%28x-1%29%29%283y%2B4%29%29 Highlight the common terms.


%28cross%28%28x-1%29%29%282y%2B5%29%29%2F%28cross%28%28x-1%29%29%283y%2B4%29%29 Cancel out the common terms.


%282y%2B5%29%2F%283y%2B4%29 Simplify.


So %282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29 simplifies to %282y%2B5%29%2F%283y%2B4%29


In other words, %282xy%2B5x-2y-5%29%2F%283xy%2B4x-3y-4%29=%282y%2B5%29%2F%283y%2B4%29


Note: One thing to point out is that the value of 'x' does not affect the final outcome of the expression since the 'x' terms cancel out. This isn't so obvious when you look at the original expression, but it becomes clear when we reach the last step.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Then you have an extraordinarily difficult task ahead of you, one for which I cannot provide any assistance nor can anyone else. The problem is you cannot "solve"



You cannot solve anything that does not have an equals sign or some sort of relational operator.

It is a rather complex rational expression that can be simplified. If that is what you meant, then follow along:

Start with the numerator polynomial. Factor an out of the first two terms and factor a -1 out of the last two terms:



Next, factor from the two terms that remain:



Next work on the denominator. Use a similar strategy, factoring out of the first two terms and -1 out of the last two terms:



And then factoring from the two terms that remain:



Eliminate the factor of that is common to both numerator and denominator leaving you with:




John