Solve rational equations

What is a rational equation?

• An equation that involves at least one rational expression, which is a fraction where the numerator and denominator are polynomials.

• An equation that only contains integers and whole numbers.

• An equation that has no variables and is always true.

• An equation that includes irrational numbers and roots.

What is an extraneous solution?

• A solution that satisfies the original equation.

• A solution that is derived from incorrect calculations.

• A solution that emerges from the process of solving an equation but does not satisfy the original equation.

• A solution that is always valid regardless of the equation.

What is the solution to the equation (x-1)/(x+2) = 3/4?

• x = 2

• x = 5/3

• x = 1

• x = 4/3

How do you check for extraneous solutions in rational equations?

• By substituting the solution back into the original equation to see if it holds true.

• By simplifying the equation before solving for the variable.

• By graphing the equation and checking the intersection points.

• By using a calculator to find approximate solutions.

How do you simplify the expression (x^2 - 1)/(x - 1)?

• x - 1

• x + 1

• x^2 + 1

• x^2 - 1

What is the solution to the equation 1/(x+4) = 1/5?

• x = -4

• x = 1

• x = -5

• x = 0

What is the solution to the equation 5/(x-2) = 1?

• x = 5

• x = 3

• x = 7

• x = 1

What is the general approach to solving rational equations?

• Identify restrictions, eliminate fractions, solve the resulting equation, and check for extraneous solutions.

• Solve the equation directly without considering restrictions.

• Only eliminate fractions and solve the equation without checking for extraneous solutions.

• Identify restrictions and solve the equation without eliminating fractions.

What is the importance of finding a common denominator in rational equations?

• It allows you to combine fractions and simplify the equation more easily.

• It helps in finding the roots of the equation directly.

• It eliminates the need for any calculations.

• It makes the fractions larger and more complex.

What is the first step in solving a rational equation?

• Identify any restrictions on the variable that would make the denominator zero.

• Multiply both sides by the least common denominator.

• Isolate the variable on one side of the equation.

• Add the numerators of the fractions.