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 quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What are domain restrictions in rational equations?

Back

Domain restrictions are values that cannot be included in the solution set of a rational equation, typically where the denominator equals zero.

Front

How do you find the least common denominator (LCD) of rational expressions?

Back

To find the LCD, factor each denominator and take the highest power of each factor that appears.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify and state any domain restrictions before proceeding to solve the equation.

Front

How do you eliminate fractions in a rational equation?

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

Front

What is the process for solving a quadratic equation?

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You can solve a quadratic equation by factoring, using the quadratic formula, or completing the square.

Front

What does it mean for a solution to be extraneous?

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An extraneous solution is a solution that does not satisfy the original equation, often introduced when manipulating the equation.

Front

How do you check your solutions in rational equations?

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Substitute the solutions back into the original equation to verify if they satisfy the equation.

Front

What is the significance of the discriminant in the quadratic formula?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real solutions; if zero, one real solution; if negative, no real solutions.