# Can this fraction be simplified further?

• trollcast
In summary, the given fraction cannot be simplified further and is already in its simplest form. The second fraction shown in the attempt at a solution is not related and cannot be simplified to the first fraction. The degree of the polynomials in the first fraction are equal while the degree of the polynomials in the second fraction are not.

Gold Member

## Homework Statement

The answer to one of my maths questions is;

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

## The Attempt at a Solution

Can this be simplified to;

$$\frac{20x^{4}-60x}{x^{3}-14x^{2}+8}$$

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.

## 1. Can fractions with different denominators be simplified?

Yes, fractions with different denominators can be simplified by finding the lowest common denominator and converting the fractions to equivalent fractions with that denominator.

## 2. How do I know if a fraction can be simplified further?

A fraction can be simplified further if the numerator and denominator have a common factor that can be divided out. You can also use the greatest common factor (GCF) to determine if a fraction can be simplified.

## 3. What is the simplest form of a fraction?

The simplest form of a fraction is when the numerator and denominator have no common factors other than 1. This is also known as the lowest terms or reduced form of a fraction.

## 4. Can mixed numbers be simplified?

Yes, mixed numbers can be simplified by converting them to improper fractions and then simplifying. After simplifying, the result can be converted back to a mixed number if desired.

## 5. Is it important to simplify fractions?

Simplifying fractions can make them easier to work with and understand. It can also help to compare fractions and perform operations on them. However, simplifying is not always necessary, especially if the fraction is already in its simplest form.