https://r2.erweima.ai/mathbot/image/1726362549602n74dzzmy.jpg

The expression you have uploaded is:

\[
\frac{4}{x+3} - \frac{2}{x+1}
\]

To solve this, we need to find a common denominator between the two fractions.

### Step 1: Find the common denominator.
The denominators are \(x+3\) and \(x+1\). The least common denominator (LCD) is the product of these two, i.e., \((x+3)(x+1)\).

### Step 2: Rewrite both fractions with the common denominator.
We will rewrite each fraction so that they both have the denominator \((x+3)(x+1)\).

\[
\frac{4}{x+3} = \frac{4(x+1)}{(x+3)(x+1)}
\]
\[
\frac{2}{x+1} = \frac{2(x+3)}{(x+3)(x+1)}
\]

### Step 3: Perform the subtraction.
Now, subtract the numerators:

\[
\frac{4(x+1)}{(x+3)(x+1)} - \frac{2(x+3)}{(x+3)(x+1)} = \frac{4(x+1) - 2(x+3)}{(x+3)(x+1)}
\]

### Step 4: Simplify the numerator.
First, expand both terms in the numerator:

\[
4(x+1) = 4x + 4
\]
\[
2(x+3) = 2x + 6
\]

Now, subtract:

\[
(4x + 4) - (2x + 6) = 4x + 4 - 2x - 6 = 2x - 2
\]

### Step 5: Final expression.
So, the simplified expression is:

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

This is the final simplified result of the expression.

Do you have any questions or would you like further details? Here are five related questions you might find useful:

1. How do you simplify complex fractions with polynomials?
2. What are the steps to find the least common denominator for rational expressions?
3. Can you explain how to factor the numerator of a rational expression?
4. How do you know when a rational expression is fully simplified?
5. What is the significance of excluded values in rational expressions?

**Tip:** Always check if the numerator can be factored further, which may allow for further simplification of the rational expression.

Perform the subtraction: \frac{4}{x+3} - \frac{2}{x+1}

Learn how to subtract two rational expressions: 4/(x+3) - 2/(x+1). This detailed solution explains finding a common denominator, rewriting the fractions, and simplifying the result. Perfect for students in Grades 8-10 studying algebra.

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