Simplifying Polynomial Fractions

[jumbogala]

Homework Statement

I need to simplify this:
((84/13)x⁴y - 4) / (-x + (21/13)x⁵)y)

Homework Equations

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?

 

[Mark44]

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

 

[jumbogala]

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

 

[Mark44]

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.

 

[oNothinGo]

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

 

[Anakin_k]

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

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.

 

[oNothinGo]

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.

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)

 

[Mark44]

Homework Statement

I need to simplify this:
((84/13)x⁴y - 4) / (-x + (21/13)x⁵)y)

Homework Equations

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?

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?