What are some challenges for rational expressions?

Also on my previous question about why are polynomials important bobpursly can you expalin it to me towards what you ment about your responce because i still do not undertand...thanks when you get a chance.

Polynomials are important for computations. Most functions are not polynomials, but polynomials are the only things we can calculate. If a computer does some computations for some finite time, it can only have added up multiplied subtracted, divided a finite number of times...

To compute functions that are not polynomials we approximate them by polynomials.

good answer.

Some challenges that you may encounter when working with rational expressions include:

1. Simplifying: Rational expressions often need to be simplified to their simplest form. This involves factoring both the numerator and denominator and canceling out common factors.

2. Finding domain restrictions: Rational expressions may have restrictions on their domain, meaning there are certain values that cannot be used as input. These restrictions are often determined by the values that make the denominator equal to zero. You need to identify these restrictions and exclude them from the domain.

3. Solving equations: When dealing with rational expressions, you may need to solve equations involving them. This can require finding a common denominator, simplifying, and isolating the variable.

4. Operations and simplification: Performing addition, subtraction, multiplication, and division operations with rational expressions can be challenging. You need to combine like terms, find common denominators, cross-cancel, and simplify the expression as much as possible.

5. Complex fractions: Rational expressions can also be in the form of complex fractions, where fractions are nested within fractions. Simplifying and performing operations with complex fractions can be tricky and require careful organization.

Regarding your previous question about why polynomials are important, the idea is that polynomials provide a way to approximate and calculate functions that are not themselves polynomials. Most functions in mathematics are not simple polynomials, but polynomials are easier to manipulate and calculate with. By approximating more complex functions with polynomials, we can perform computations, analyze behavior, and solve problems that would otherwise be difficult or impossible.

For example, if you wanted to find the value of a function at a specific point, you could use a polynomial approximation of that function to get an approximate value. This is particularly useful when dealing with computational methods and numerical analysis in areas such as physics, engineering, economics, and computer science.

Polynomials also have a variety of properties and theorems that make them important in algebra, calculus, and other branches of mathematics. They provide a foundation for understanding concepts like roots, factors, equations, graphs, and systems of equations.

In summary, polynomials are important because they provide a versatile and effective tool for approximating, calculating, and analyzing a wide range of functions and mathematical concepts.