Solving Rational Equations

Front

What is a rational equation?

Back

A rational equation is an equation that involves at least one rational expression, which is a fraction where the numerator and denominator are polynomials.

Front

What are the steps to solve a rational equation?

Back

1. Identify the rational expressions. 2. Find a common denominator. 3. Multiply both sides by the common denominator to eliminate fractions. 4. Solve the resulting equation. 5. Check for extraneous solutions.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

How do you find the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator equals zero.

Front

What are the domain restrictions for the rational expression 1/(x-3)?

Back

x ≠ 3.

Front

What are the domain restrictions for the rational expression 1/(x^2-4)?

Back

x ≠ 2, x ≠ -2.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

How do you apply the quadratic formula to the equation x² - 5x + 6 = 0?

Back

Using the quadratic formula: a=1, b=-5, c=6. Solutions are x = 2 and x = 3.

Front

What is the first step in solving the equation (2/x) + (3/(x-1)) = 1?

Back

Find a common denominator, which is x(x-1).

Front

What happens if you ignore domain restrictions when solving rational equations?

Back

Ignoring domain restrictions can lead to extraneous solutions that do not satisfy the original equation.