Question

1. # Simplify The Rational Expression. State Any Restrictions On The Variable. N^4-10N^2+24/N^4-9N^2+18

Rational expressions are mathematical expressions that contain fractions. They can be simplified in order to make them easier to work with or understand. In this blog post, we will explore the simplification of a rather complex rational expression, as well as its restrictions on the variable. We’ll also discuss how to use this approach when simplifying other rational expressions. Keep reading to learn more!

## What is a rational expression?

A rational expression is an algebraic expression that can be written as a quotient of two polynomials. In other words, it is a fraction whose numerator and denominator are both polynomials. The variable in a rational expression can have any value except for the values that would make the denominator equal to zero.

## What is the process of simplifying a rational expression?

When simplifying a rational expression, the first step is to factor both the numerator and denominator. Next, cancel out any common factors between the numerator and denominator. Finally, reduce any remaining fractions. Any restrictions on the variable must be stated at this point.

## How do you know when you have a simplified expression?

In order to have a simplified expression, the numerator and denominator should have no common factors. Additionally, all exponents in the rational expression should be positive.

## What are the restrictions on the variable in this equation?

There are restrictions on the variable in this equation. The variable cannot be negative and the numerator and denominator cannot both be zero. These restrictions make the equation undefined.

## Conclusion

In this article, we discussed how to simplify a rational expression and the restrictions on the variable. Specifically, we looked at the rational expression N^4-10N^2+24/N^4-9N^2+18. After breaking down each part of the equation and combining like terms, we came up with our simplified answer of 6/3. The only restriction on the variable is that N cannot be equal to zero since division by zero is not defined in mathematics. We hope this information has been useful for helping you understand simplifying rational expressions!

2. Simplifying rational expressions can be a real head-scratcher – but don’t worry, we’ve got your back!

Let’s take a look at this expression:

N^4-10N^2+24/N^4-9N^2+18

To simplify this expression, we need to factor both the numerator and denominator by finding the greatest common factor (GCF) between them.

The greatest common factor between N^4-10N^2+24 and N^4-9N^2+18 is N^2-6.

We can now factor out N^2-6 from both the numerator and denominator, and then divide both the numerator and denominator by the factor.

This simplifies the expression to: (N^2+4)/(N^2-3)

Now, this expression can be further simplified by dividing both the numerator and denominator by the GCF of N+2 and N-2.

The final simplified expression is: (N+2)/(N-2)

The restriction on the variable N is that it cannot be equal to 2.

There you have it – now you know how to simplify rational expressions and the restrictions imposed on the variable!