## Tutoring on Solving Rational Equations

Learning Objectives:

#### Understand to Solve Rational Equations.

Math Tutoring on Solving Rational Equations

Equations that contain rational expressions are called rational equations. Here are the guidelines for solving rational equations.

Step 1: We will factor all the denominators.

Step 2: We will determine the least common denominator or LCD and then multiply each side of the equation by the LCD.
Step 3:
We will solve the resulting equation.

Step 4: Then, we will check our solutions. We need to be aware that if what appears to be a solution makes a denominator equal to zero, we must exclude that value. These types of answers are called extraneous solutions.

Step 5: Lastly, we can check our solutions on the graphing calculator. If we type the left side of the equation in y1 and the right side of the equation in y2, we can check our solutions by finding the point of points of intersection of the two graphs.  Therefore we solve rational equations by finding LCD. We can then follow either of two procedures. We can rewrite the equation so that all terms have the LCD and we can solve for the variable with just the numerators. Or we can multiply both sides of the equation by the LCD so that all terms become polynomials instead of rational expressions.

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Hook questions:

1.    What is the definition of rational equations?

2.    How do you solve a multi-step equation?

3.    What are the steps used to solve an equation with rational expressions?

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