Solving Rational Equations in Pre Calculus

What is the first step in solving a rational equation?

• Identify the denominator

• Multiply both sides by the least common multiple

• Find the excluded values

• Factor the equation

What is the result of 4x + 7 = 7x - 28 after simplification?

• x = 7/4

• x = 4/7

• x = 28/3

• x = 35/3

Why are excluded values important in rational equations?

• They are necessary for factoring

• They determine the highest value of x

• They can lead to undefined expressions

• They simplify the equation further

What does the zero product property allow us to do?

• Multiply both sides by zero

• Find the least common multiple

• Cancel out terms

• Set each factor equal to zero

What is the solution to the equation when factoring 4n squared plus 12n minus 10?

• n = -1, n = -5

• n = -1, n = 5

• n = 5, n = -1/4

• n = -1, n = -5/4

How do you solve a rational equation with different denominators?

• By subtracting one denominator from the other

• By adding the denominators

• By finding the least common multiple

• By dividing both sides by the highest denominator

What is the significance of distributing a negative across an equation?

• It identifies the excluded values

• It simplifies the equation

• It changes the signs of the terms

• It eliminates the need for factoring

What is the correct approach to solve 5m squared subtract 2m plus 23m equals 26?

• Factoring by grouping

• Using the quadratic formula

• Finding the least common multiple

• Setting each term equal to zero

What are the excluded values in an equation with denominators m plus 2 and m plus 3?

• m = 1

• m = 2, m = 3

• m = -2, m = -3

• m = 0

Why is it necessary to check solutions against excluded values?

• To find more solutions

• To simplify the equation further

• To practice factoring

• To ensure the solution is not undefined