Question

morgan made a mistake when subtracting the rational expressions.\\(\frac{3t^2 - 4t + 1}{t + 3}-\frac{t^2 + 2t + 2}{t + 3}=\frac{2t^2 - 2t + 3}{t + 3}\\)\
what was morgan’s error?\
morgan forgot to cancel out the +3 in the numerator and denominator as her final step.\
morgan forgot to combine only like terms.\
morgan forgot to distribute the negative sign to two of the terms in the second expression.\
morgan forgot to subtract the denominators as well as the numerators.

Explanation:

Step1: Correctly subtract numerators

When subtracting $\frac{3t^2-4t+1}{t+3} - \frac{t^2+2t+2}{t+3}$, distribute the negative sign to all terms in the second numerator:
$\frac{(3t^2-4t+1) - (t^2+2t+2)}{t+3} = \frac{3t^2-4t+1 - t^2 -2t -2}{t+3}$

Step2: Combine like terms

Simplify the numerator:
$\frac{(3t^2-t^2)+(-4t-2t)+(1-2)}{t+3} = \frac{2t^2-6t-1}{t+3}$

Step3: Compare to Morgan's result

Morgan got $\frac{2t^2-2t+3}{t+3}$. This matches the error of not distributing the negative sign to all terms in the second numerator (only the first term was subtracted, the others were incorrectly added).

Answer:

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