Express in simplest form. Show all steps to receive credit for your answer. 2d²-2d-40 d²-4d-5 d²+7d+12 d²+2d-3 Paragraph V BI UVA |||| < !!!! ·|| O + v ... 11.
Express in simplest form. Show all steps to receive credit for your answer. 2d²-2d-40 d²-4d-5 d²+7d+12 d²+2d-3 Paragraph V BI UVA |||| < !!!! ·|| O + v ... 11.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![### Simplifying Rational Expressions
Express in simplest form. Show all steps to receive credit for your answer.
\[
\frac{2d^2 - 2d - 40}{d^2 + 7d + 12} \div \frac{d^2 - 4d - 5}{d^2 + 2d - 3}
\]
To simplify this problem, follow these steps:
1. **Factor the numerators and denominators:**
- For \(\frac{2d^2 - 2d - 40}{d^2 + 7d + 12}\):
- Numerator: \(2d^2 - 2d - 40\)
- Denominator: \(d^2 + 7d + 12\)
Factor the numerator and denominator:
\[
2d^2 - 2d - 40 = 2(d^2 - d - 20) = 2(d - 5)(d + 4)
\]
\[
d^2 + 7d + 12 = (d + 3)(d + 4)
\]
Thus,
\[
\frac{2(d - 5)(d + 4)}{(d + 3)(d + 4)}
\]
- For \(\frac{d^2 - 4d - 5}{d^2 + 2d - 3}\):
- Numerator: \(d^2 - 4d - 5\)
- Denominator: \(d^2 + 2d - 3\)
Factor the numerator and denominator:
\[
d^2 - 4d - 5 = (d - 5)(d + 1)
\]
\[
d^2 + 2d - 3 = (d + 3)(d - 1)
\]
Thus,
\[
\frac{(d - 5)(d + 1)}{(d + 3)(d - 1)}
\]
2. **Rewrite the division as multiplication by the reciprocal:**
\[
\frac{2(d - 5)(d + 4)}{(d + 3)(d + 4)} \div \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd66c9551-2207-4a1f-96cc-82c211723c9b%2Fd4a2d856-6993-49c7-bdf7-f870db53c5ab%2Ftgqsv55_processed.png&w=3840&q=75)
Transcribed Image Text:### Simplifying Rational Expressions
Express in simplest form. Show all steps to receive credit for your answer.
\[
\frac{2d^2 - 2d - 40}{d^2 + 7d + 12} \div \frac{d^2 - 4d - 5}{d^2 + 2d - 3}
\]
To simplify this problem, follow these steps:
1. **Factor the numerators and denominators:**
- For \(\frac{2d^2 - 2d - 40}{d^2 + 7d + 12}\):
- Numerator: \(2d^2 - 2d - 40\)
- Denominator: \(d^2 + 7d + 12\)
Factor the numerator and denominator:
\[
2d^2 - 2d - 40 = 2(d^2 - d - 20) = 2(d - 5)(d + 4)
\]
\[
d^2 + 7d + 12 = (d + 3)(d + 4)
\]
Thus,
\[
\frac{2(d - 5)(d + 4)}{(d + 3)(d + 4)}
\]
- For \(\frac{d^2 - 4d - 5}{d^2 + 2d - 3}\):
- Numerator: \(d^2 - 4d - 5\)
- Denominator: \(d^2 + 2d - 3\)
Factor the numerator and denominator:
\[
d^2 - 4d - 5 = (d - 5)(d + 1)
\]
\[
d^2 + 2d - 3 = (d + 3)(d - 1)
\]
Thus,
\[
\frac{(d - 5)(d + 1)}{(d + 3)(d - 1)}
\]
2. **Rewrite the division as multiplication by the reciprocal:**
\[
\frac{2(d - 5)(d + 4)}{(d + 3)(d + 4)} \div \
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