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What is the definition of solving a rational equation?
to find the unknown variables
Can the five steps for solving rational equation be eliminated?
no. an individual step might be, but not all.
When solving an algebraic equation which operands do you perform first?
In algebra, you perform the operations inside parentheses first.
What method is used for solving a rational equation?
Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
Is an equation that contains one or more rational expressions?
Yes, an equation that contains one or more rational expressions is called a rational equation. A rational expression is a fraction where the numerator and/or denominator are polynomials. For example, the equation (\frac{x + 1}{x - 2} = 3) is a rational equation because it includes the rational expression (\frac{x + 1}{x - 2}). Solving such equations often involves finding a common denominator and addressing any restrictions on the variable to avoid division by zero.
What is the definition of solving a rational equation?
to find the unknown variables
When solving a rational equation what is the first step you must always take?
Get rid of the denominator.
Can the five steps for solving rational equation be eliminated?
no. an individual step might be, but not all.
When solving a rational equation why is it necessary to perform a check?
It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.
When solving an algebraic equation which operands do you perform first?
In algebra, you perform the operations inside parentheses first.
Can any steps to solving a rational equation be eliminated?
Yes, but it depends on your mathematical skills and confidence.
What method is used for solving a rational equation?
Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
Can you change any of the steps for solving a rational equation?
Yes. Since "these" do not exist, cjanging them should not make a difference.
Is an equation that contains one or more rational expressions?
Yes, an equation that contains one or more rational expressions is called a rational equation. A rational expression is a fraction where the numerator and/or denominator are polynomials. For example, the equation (\frac{x + 1}{x - 2} = 3) is a rational equation because it includes the rational expression (\frac{x + 1}{x - 2}). Solving such equations often involves finding a common denominator and addressing any restrictions on the variable to avoid division by zero.
How is an extraneous solution of a ration equation similar to an excluded value of a rational equation?
An extraneous solution of a rational equation is a solution that emerges from the algebraic process but does not satisfy the original equation, while an excluded value is a value that makes the denominator zero and is therefore not permissible in the equation. Both concepts highlight the limitations and constraints of rational expressions. Excluded values can lead to extraneous solutions if they are mistakenly included in the solution set. Thus, both are essential to consider when solving rational equations to ensure valid solutions.
What are the steps in solving rational equations?
1. First we need to determine the least common denominator of the fractions in the given rational equation. 2. We need to take out the fractions by multiplying All terms by the least common denominator. 3. Then we have to simplify the terms in rational equation. 4. Solve the resulting equation. 5. Check the answers to make confident the solution does not make the fraction undefined.
What role of operations that applies when you are solving an equation does not apply when your solving an inequality?
What role of operations that applies when you are solving an equation does not apply when your solving an inequality?"
