Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Morgan made a mistake when subtracting the rational expressions below 3t^2-4t+1/t+3-t^2+2t+2/t+3=2t^2-2t+3/t+3. What was Morgan's error?

A. Morgan forgot to combine only like terms
B. Morgan forgot to subtract the denominators as well as numerators.
C. Morgan forgot to cancel out the +3 in the numerator and denominator as her final step.
D. Morgan forgot to distribute the negative sign to two of the terms in the second expression.

Sagot :

Answer: Choice D.

Morgan forgot to distribute the negative sign to two of the terms in the second expression.

=============================================================

Explanation:

Focus on the numerators.

We have (3t^2-4t+1) as the first numerator and we subtract off (t^2+2t+2) as the second numerator.

Morgan needs to simplify (3t^2-4t+1)-(t^2+2t+2) for the numerator.

Mistakenly, she had these steps

(3t^2-4t+1)-(t^2+2t+2)

3t^2-4t+1-t^2+2t+2 .... her mistake made here

(3t^2-t^2)+(-4t+2t)+(1+2)

2t^2-2t+3

All of this applies to the numerator. The denominator stays at t+3 the entire time. So effectively we can ignore it on a temporary basis.

Here's what Morgan should have for her steps when simplifying the numerator.

(3t^2-4t+1)-(t^2+2t+2)

3t^2-4t+1-t^2-2t-2 ..... distribute the negative

(3t^2-t^2)+(-4t-2t)+(1-2)

2t^2-6t-1

Note in the second step, the negative outside flips the sign of each term in the second parenthesis.

Therefore,

[tex]\frac{3t^2-4t+1}{t+3}-\frac{t^2+2t+2}{t+3}\\\\\frac{(3t^2-4t+1)-(t^2+2t+2)}{t+3}\\\\\frac{3t^2-4t+1-t^2-2t-2}{t+3}\\\\\frac{2t^2-6t-1}{t+3}\\\\[/tex]

which means [tex]\frac{3t^2-4t+1}{t+3}-\frac{t^2+2t+2}{t+3}=\frac{2t^2-6t-1}{t+3}, \ \ \text{ where } t \ne -3\\\\[/tex]

Side notes:

  • The fractions can only be subtracted since the denominators are the same.
  • We have [tex]t \ne -3[/tex] to avoid a division by zero error.
  • Rational expressions are a fraction, or ratio, of two polynomials.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.