I thought that we can solve anything with equations is it always polynomials. Isn't this the same thing as finding the unknown for an equation. As i said in my previous message or am i wrong.
Also what about the rational expressions what are some challenges about working with them?
No, we can solve many other equations. Log and Trig for instance.
Some equations have no known solutions.
Please don't put volunteers name in the subject: a lot of folks who could answer don't bother. What if the ppeople you put in the subject line are gone? You have shot yourself in the foot.
You are correct that equations can be used to solve a wide range of problems, not just limited to polynomials. Equations represent a relationship between variables, and by rearranging the equation, we can find the value of the unknown variable(s) that satisfy the equation.
Polynomial equations are just one type of equation, where the unknown variable(s) are raised to integer powers. However, there are many other types of equations that can be solved using different mathematical techniques. Logarithmic and trigonometric equations, for example, involve logarithms and trigonometric functions and require different methods to solve.
Rational expressions are equations that involve fractions with polynomials as the numerator and denominator. Working with rational expressions can present various challenges:
1. Simplification: Rational expressions may need to be simplified before attempting to solve them. This involves factoring both the numerator and denominator and canceling out any common factors to simplify the expression.
2. Domain Restrictions: Rational expressions may have restrictions on the values that the variable(s) can take. Division by zero, for instance, is not defined, so any value that makes the denominator zero should be excluded from the solution set.
3. Extraneous Solutions: Sometimes, solving a rational expression can introduce extraneous solutions, which are solutions that do not satisfy the original equation. These solutions can occur when we perform operations, like squaring both sides or multiplying both sides by an expression that may introduce additional solutions.
4. Complex Numbers: Rational expressions can have solutions that involve complex numbers (numbers involving the square root of -1). Dealing with complex numbers requires a different way of representing and interpreting solutions compared to real numbers.
It's important to keep these challenges in mind when working with rational expressions and to always check solutions for validity by substituting them back into the original equation.