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Answer :
Let's look at the problem where Morgan is subtracting two rational expressions:
[tex]\[
\frac{3t^2 - 4t + 1}{t+3} - \frac{t^2 + 2t + 2}{t+3}
\][/tex]
Both rational expressions have the same denominator, [tex]\(t+3\)[/tex]. When subtracting fractions with the same denominator, you simply subtract the numerators and keep the common denominator.
Here's how it should be done step by step:
1. Subtract the Numerators:
You need to subtract the second numerator from the first numerator:
[tex]\[
(3t^2 - 4t + 1) - (t^2 + 2t + 2)
\][/tex]
2. Distribute the Negative Sign:
This is a crucial step where Morgan made a mistake. When you subtract the second numerator, you must distribute the negative sign across all terms in that numerator:
[tex]\[
3t^2 - 4t + 1 - t^2 - 2t - 2
\][/tex]
3. Combine Like Terms:
Now, combine the like terms:
- [tex]\(3t^2 - t^2 = 2t^2\)[/tex]
- [tex]\(-4t - 2t = -6t\)[/tex]
- [tex]\(1 - 2 = -1\)[/tex]
So, the correct numerator after combining like terms is:
[tex]\[
2t^2 - 6t - 1
\][/tex]
4. Write the Correct Expression:
The correct result for the subtraction is:
[tex]\[
\frac{2t^2 - 6t - 1}{t+3}
\][/tex]
Morgan's mistake was in the distribution of the negative sign. She didn't distribute it correctly across all terms in the second numerator. Therefore, the correct error is that Morgan forgot to distribute the negative sign to two of the terms in the second expression.
[tex]\[
\frac{3t^2 - 4t + 1}{t+3} - \frac{t^2 + 2t + 2}{t+3}
\][/tex]
Both rational expressions have the same denominator, [tex]\(t+3\)[/tex]. When subtracting fractions with the same denominator, you simply subtract the numerators and keep the common denominator.
Here's how it should be done step by step:
1. Subtract the Numerators:
You need to subtract the second numerator from the first numerator:
[tex]\[
(3t^2 - 4t + 1) - (t^2 + 2t + 2)
\][/tex]
2. Distribute the Negative Sign:
This is a crucial step where Morgan made a mistake. When you subtract the second numerator, you must distribute the negative sign across all terms in that numerator:
[tex]\[
3t^2 - 4t + 1 - t^2 - 2t - 2
\][/tex]
3. Combine Like Terms:
Now, combine the like terms:
- [tex]\(3t^2 - t^2 = 2t^2\)[/tex]
- [tex]\(-4t - 2t = -6t\)[/tex]
- [tex]\(1 - 2 = -1\)[/tex]
So, the correct numerator after combining like terms is:
[tex]\[
2t^2 - 6t - 1
\][/tex]
4. Write the Correct Expression:
The correct result for the subtraction is:
[tex]\[
\frac{2t^2 - 6t - 1}{t+3}
\][/tex]
Morgan's mistake was in the distribution of the negative sign. She didn't distribute it correctly across all terms in the second numerator. Therefore, the correct error is that Morgan forgot to distribute the negative sign to two of the terms in the second expression.
Thanks for taking the time to read Morgan made a mistake when subtracting the rational expressions below tex frac 3t 2 4t 1 t 3 frac t 2 2t 2 t 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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