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Rational Equations
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What is a rational equation?
A rational equation is an equation that contains one or more rational expressions.
How do you solve a rational equation?
To solve a rational equation, find a common denominator, eliminate the fractions, then solve the resulting equation.
What must you check for after solving a rational equation?
Check for extraneous solutions because multiplying by the common denominator may introduce false solutions.
What is a rational expression?
A rational expression is a ratio of two polynomials.
Give an example of a simple rational equation.
An example is (x/2) + (3/x) = 1.
How can rational equations be useful?
Rational equations are used in real-life problems involving rates, such as speed, work, or fluid flow.
What is extraneous solution?
An extraneous solution is a solution derived from an equation that is not valid for the original equation.
What precautions should you take when solving rational equations?
Avoid solutions that make any denominator zero.
Why is finding a common denominator important in solving rational equations?
It allows you to eliminate fractions to simplify the equation.
What happens if you divide by zero in a rational equation?
Dividing by zero is undefined, so it makes the equation invalid.
What do you do if different denominators appear in a rational equation?
Multiply each term by the least common denominator to eliminate the fractions.
How is solving x/(x-1) = 2 done?
Multiply each side by (x-1), then solve: x = 2(x-1).
What should you do if your solution makes a denominator zero?
Discard that solution as it is extraneous.
Explain the term 'least common denominator' in context of rational equations.
It is the smallest expression that all denominators in the equation can divide into without a remainder.
What is a polynomial?
A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
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