Simplifying and Solving Rational Eqquations

In today’s lesson, we explore rational functions and rational equations step by step in a clear and simple way. We begin by understanding that a rational function has the form f(x) = \frac{p(x)}{q(x)}, where both p(x) and q(x) are polynomials, and very importantly, q(x) \neq 0. This restriction helps us identify values that are not allowed in the domain. Next, we focus on how to simplify rational expressions. By factoring the numerator and denominator, we can reduce expressions and better understand their structure. This step is essential before solving any rational equation. Finally, we solve a rational equation step by step using the example: 2/(x-10)- 3/(x-2)= 6/(x^2 - 12x + 20) We learn how to: Factor the denominator x^2 - 12x + 20 = (x - 10)(x - 2) Identify restrictions (values that make the denominator zero) Multiply both sides by the least common denominator (LCD) to eliminate fractions Solve the resulting equation Check solutions to make sure they are valid and not excluded from the domain This lesson builds a strong foundation for working with rational equations and helps students avoid common mistakes. Step by step, you will gain confidence in simplifying and solving these types of problems. Perfect for students who want a clear and structured approach to rational expressions and equations.