Rational Expressions and Equations

What is the initial step for both adding/subtracting rational expressions and solving rational equations?

• Factoring the denominators

• Getting common denominators

• Adding the numerators

• Cross-multiplying

What is the factored form of the denominator x^2 - 9?

• (x-3)(x-3)

• (x+3)(x+3)

• (x+3)(x-3)

• x(x-9)

After simplifying the rational equation and setting it to zero, what quadratic equation is obtained?

• x^2 + 5x + 6 = 0

• x^2 - 5x + 6 = 0

• x^2 - 5x - 6 = 0

• x^2 + 5x - 6 = 0

Given the solutions x=2 and x=3, which solution is considered extraneous for the original rational equation?

• x = 2

• x = 3

• Both x=2 and x=3

• Neither x=2 nor x=3

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After clearing the denominators, the equation x/(x-3) + 4/x = (x+3)/(x-3) simplifies to which of the following?

• x^2 + 4x - 12 = x^2 + 3x

• x^2 + 4x + 12 = x^2 + 3x

• x^2 - 4x + 12 = x^2 - 3x

• x^2 - 4x - 12 = x^2 - 3x

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

• 3

• 0

• 12

• -12

What is the solution to the equation (2x-3)/(x-1) = (8x+1)/(4x+5)?

• -14/5

• -14/9

• 14/9

• 14/5

Kyle mows a lawn in 50 minutes. If Jeff helps him, they finish in 20 minutes. Which equation represents the time (x) it would take Jeff to mow the lawn alone?

• 1/50 - 1/x = 1/20

• 1/50 + 1/x = 1/20

• 50 + x = 20

• 1/50 + 1/20 = 1/x

Morgan assembles 2 care packages in 10 minutes, and Jordan assembles 3 in 21 minutes. If they need to assemble 20 packages together, which equation represents the total time (x) it would take them?

• (10/2) + (21/3) = x/20

• (2/10) + (3/21) = 20/x

• (2/10) + (3/21) = x/20

• (10/2) + (21/3) = 20/x