Solving Rational Expressions in Algebra 2

What is the main goal when solving rational equations?

• To factor the denominator

• To eliminate the fractions

• To find the common denominator

• To simplify the numerator

What does cross-multiplication help to achieve in rational equations?

• It helps to divide fractions

• It helps to eliminate fractions

• It helps to add fractions

• It helps to subtract fractions

In the example problem, what is the first step after setting up the equation?

• Divide both sides by the necessary terms

• Add the fractions

• Multiply both sides by the necessary terms

• Subtract the fractions

Why is it important to check the solutions in rational equations?

• To find the common denominator

• To simplify the equation further

• To verify the denominator does not become zero

• To ensure the numerator is correct

What should you do if the denominator becomes zero in a solution?

• Accept the solution

• Ignore the solution

• Reject the solution

• Simplify the solution

In the second example, what is the purpose of multiplying each term by the necessary factors?

• To add the fractions

• To eliminate the fractions

• To divide the fractions

• To subtract the fractions

What is the result of distributing the terms in the second example?

• 12x = x^2 + 7x + 12x + 84

• 12x = x^2 - 7x - 12x + 84

• 12x = x^2 + 7x - 12x - 84

• 12x = x^2 - 7x + 12x - 84

What is the next step after factoring the equation in the final example?

• Set each factor equal to zero

• Add the factors

• Multiply the factors

• Divide the factors

Why is it important to check for extraneous solutions?

• To simplify the equation further

• To ensure the numerator is correct

• To find the common denominator

• To verify the denominator does not become zero

What is the final step in solving a rational equation?

• Multiply the fractions

• Add the fractions

• Subtract the fractions

• Verify the solutions