Simplifying and Multiplying Rational Expressions

What is a rational function?

• A polynomial function

• A type of exponential function

• A function based on rational numbers

• A quotient of two polynomials

What happens if the denominator in a rational function equals zero?

• The function is undefined

• The function equals one

• The function becomes an integer

• The function simplifies further

What must be true for a rational function to be simplified correctly?

• The denominator must be zero

• The function must contain variables

• Any common factors must be cancelled out

• The numerator must be larger than the denominator

Why is factoring important in simplifying rational expressions?

• It is only necessary for complex functions

• It makes the numbers larger

• It changes the variables in the expression

• It helps in reducing the expression to its simplest form

What is the result of simplifying 3x^7 / 2x^4?

• 5x^3

• 3x^3 / 2

• x^11 / 2

• x^3 / 6

How do you handle a situation where the factors are subtracted in reverse order?

• Multiply by -1

• Factor out a negative one to correct the order

• Ignore the signs and simplify

• Leave them as they are

What does cross-canceling involve in the context of multiplying rational functions?

• Canceling out common factors across numerators and denominators

• Adding factors from the numerator and denominator

• Multiplying factors diagonally across the function

• Subtracting common factors before multiplying

What is the correct method to divide rational expressions?

• Divide the numerators and multiply the denominators

• Subtract the divisor from the dividend

• Add the divisor to the dividend

• Multiply by the reciprocal of the divisor

What should you always check after simplifying a rational equation?

• If the solution is a whole number

• If the solution works in the original equation

• If the solution is positive

• If the equation is linear

What is an extraneous solution in the context of rational equations?

• A solution that does not satisfy the original equation

• A necessary solution for all rational equations

• A solution that simplifies the equation

• The only solution to the equation