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/or denominator are polynomials.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify any restrictions on the variable that would make the denominator zero.

Front

How do you eliminate fractions in a rational equation?

Back

Multiply both sides of the equation by the least common denominator (LCD) to eliminate the fractions.

Front

What is the quadratic formula?

Back

Front

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its lowest terms by canceling common factors in the numerator and denominator.

Front

What is a common mistake when solving rational equations?

Back

A common mistake is not checking for extraneous solutions that may arise after multiplying by the LCD.

Front

How do you check if a solution is valid in a rational equation?

Back

Substitute the solution back into the original equation to ensure it does not make any denominator zero.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, where all equations are satisfied simultaneously.

Front

What is the process of solving a system of equations graphically?

Back

Graph each equation on the same coordinate plane and identify the point(s) where the graphs intersect.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation correspond to the x-intercepts of its graph, where the graph crosses the x-axis.