# Simplifying Polynomials

1. Oct 10, 2009

### jumbogala

1. The problem statement, all variables and given/known data
I need to simplify this:
((84/13)x4y - 4) / (-x + (21/13)x5)y)

2. Relevant equations

3. The attempt at a solution
I don't know if it can be simplified further. I can't factor anything out that will cancel. I multiplied both the top and the bottom by 13 to get rid of those fractions and got

(84x4y - 52) / (-13x + 21x5y) but that didn't make a solution jump out at me.

Help?

Last edited: Oct 10, 2009
2. Oct 10, 2009

### Staff: Mentor

I don't see anything either, but the -13 in the denominator should be -13x.

3. Oct 10, 2009

### jumbogala

Oh right, thanks. I guess it can't be simplified then?

4. Oct 10, 2009

### Staff: Mentor

With a closer look, yes, it can be simplified a lot more.
$$\frac{84x^4y - 52}{(-13x + 21x^5y}~=~\frac{4(21x^4y - 13)}{x(21x^4y - 13)}~=~\frac{4}{x}$$
This assumes, of course, that 21x4y - 13 != 0.

5. Oct 11, 2009

### oNothinGo

Here is what I got:
[(84x4y-52)/13] / (-xy + (21/13)x5y)
= [(84x4y-52)/13] / [(-13xy + 21x5y)/13]
= (84x4y-52) / (-13xy + 21x5y)

6. Oct 11, 2009

### Anakin_k

But the numerator and denominator can be factored a bit more. Factor out the 4 in the numerator and the x in the denominator. You should get:

4(21x4y-13) / x(21x4y-13)

The (21x4y-13) from the top and the bottom divide out and you are left with 4/x. The restrictions would be (21x4y-13) is not equal to zero and x is not equal to zero.

Mark44 got it perfectly right.

7. Oct 11, 2009

### oNothinGo

if you factor out x in the denominator, you will get x(21x4y-13y), not x(21x4y-13).
oh nvm.
Because Jumbogala wrote (-x + (21/13)x5)y), so I thought the y times (-x + (21/13)x5), which equals to (-xy + (21/13)x5y)

8. Oct 11, 2009

### Staff: Mentor

In my earlier response, I simplified the final expression you showed, but didn't verify that it was the same as the original expression (it isn't). There is an extra right parenthesis in denominator of the first expression, so it's difficult to tell exactly what the original problem is. With that extra parenthesis, it's unclear whether that final y in the denominator multiplies only the x5 term or both terms in the denominator.

Can you clear this up for us?