https://file.aiquickdraw.com/mathbot/file/17259903032535d6vj2iv.jpg

The image you provided contains the following expressions:

1. \( \frac{1}{2x+3} \)
2. \( \frac{1}{2x+1} - \frac{1}{2x+3} \)

For the second expression, we can simplify this by finding a common denominator:

\[
\frac{1}{2x+1} - \frac{1}{2x+3} = \frac{(2x+3) - (2x+1)}{(2x+1)(2x+3)} = \frac{2}{(2x+1)(2x+3)}
\]

This simplification shows that the difference between these two fractions is \(\frac{2}{(2x+1)(2x+3)}\).

Would you like further details or have any questions about this process?

Related questions:
1. How would you integrate \(\frac{1}{2x+3}\)?
2. Can you solve for \(x\) when \(\frac{1}{2x+1} - \frac{1}{2x+3} = 0\)?
3. What happens to the value of \(\frac{1}{2x+1} - \frac{1}{2x+3}\) as \(x\) approaches infinity?
4. How do you factorize a quadratic expression like \((2x+1)(2x+3)\)?
5. What are the vertical asymptotes of the function \(\frac{2}{(2x+1)(2x+3)}\)?

**Tip:** When simplifying expressions involving fractions with different denominators, always try to find a common denominator, as it simplifies the subtraction or addition.

Simplify the expression: \( \frac{1}{2x+1} - \frac{1}{2x+3} \)

Learn how to simplify the rational expression \( \frac{1}{2x+1} - \frac{1}{2x+3} \) by finding a common denominator. This problem involves algebraic concepts such as fractions, common denominators, and rational expressions. Suitable for students in Grades 9-10.

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