Can this fraction be simplified further?

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The fraction $$\frac{60x^{4}-240x}{3x^{4}+x^{3}-14x^{2}+4x+8}$$ cannot be simplified to $$\frac{20x^{4}-60x}{x^{3}-14x^{2}+8}$$ as the degrees of the polynomials differ. The first fraction is already in its simplest form, with both the numerator and denominator having equal degrees of 4. A key point in verifying simplification is comparing the degrees of the polynomials involved. The discussion highlights the importance of checking polynomial degrees when simplifying fractions. Understanding these concepts ensures accurate simplification in mathematical expressions.
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Homework Statement



The answer to one of my maths questions is;

$$\frac{60x^{4}-240x}{3x^{4}+x^{3}-14x^{2}+4x+8} $$

Homework Equations





The Attempt at a Solution



Can this be simplified to;

$$\frac{20x^{4}-60x}{x^{3}-14x^{2}+8} $$
 
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The first fraction you show seems to be in the simplest form. It can't be simplified to the 2nd fraction. If you want to know where you went wrong, you might try showing the steps you took to get there.
 
One indication that they are not related is the first fraction has equal degrees (4), while the second does not (4, 3).
 
Thanks, I forgot about comparing the degree of the polynominals to check my answer.

I know the steps before it are right, I was just checking I'd got the answer into its simplest form.
 
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