P(t)-2+7/2 +7t a2-7 2t+2/2 (aP-1)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you explain how to simplify this equation (the image)?

I believe it could be simplified to (4P + (14P-49)t)/(4+(4P-14)t). 

In my typed response, P represents P nought.

The image contains handwritten notes on a mathematical expression, possibly a simplification or transformation of an equation. The content is as follows:

1. The original expression at the top is written as:

   \[ P(t) = 2 + \frac{14}{2p - 7} + 7t \]

   This section is crossed out, indicating it might be an erroneous step or one that is being revised.

2. The corrected expression is shown below:

   \[
   P(t) = 2 + 7 \left(\frac{2}{2p - 7}\right) + 7t
   \]

3. There is also another term expressed with a similar denominator:
   
   \[
   2t + 2 \left(\frac{2}{2p - 7}\right)
   \]

This work likely represents algebraic manipulation involving combining or simplifying rational expressions with a common denominator. There are no graphs or diagrams provided.
Transcribed Image Text:The image contains handwritten notes on a mathematical expression, possibly a simplification or transformation of an equation. The content is as follows: 1. The original expression at the top is written as: \[ P(t) = 2 + \frac{14}{2p - 7} + 7t \] This section is crossed out, indicating it might be an erroneous step or one that is being revised. 2. The corrected expression is shown below: \[ P(t) = 2 + 7 \left(\frac{2}{2p - 7}\right) + 7t \] 3. There is also another term expressed with a similar denominator: \[ 2t + 2 \left(\frac{2}{2p - 7}\right) \] This work likely represents algebraic manipulation involving combining or simplifying rational expressions with a common denominator. There are no graphs or diagrams provided.
Expert Solution
Step 1

Consider the given function as Pt=2+722P0-7+7t2t+222P0-7.

The right hand side expression of the above function is 2+722P0-7+7t2t+222P0-7.

The numerator 2+722P0-7+7t can be simplified as follows.

2+722P0-7+7t=2+7×22P0-7+7t=2×2P0-72P0-7+142P0-7+7t×2P0-72P0-7=4P0-142P0-7+142P0-7+14tP0-49t2P0-7=4P0-14+14+14tP0-49t2P0-7=4P0+14P0-49t2P0-7

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