The difference for the x+5/x+2-x+1/x^2+2x expression is – **x ^{2} + 4x – 1 / x^{2} + 2**. Lets find out the solution step-by-step.

### Problem

Simplify the expression: x+5/x+2-x+1/x^2+2x

## Step-by-Step Solution

### Step 1: Factor the Denominators

First, observe the denominators of both fractions:

- The denominator of the first fraction is (x+2), which cannot be factored further.
- The denominator of the second fraction is (x
^{2}+2x), which can be factored as:

This will help us later in finding a common denominator.

### Step 2: Identify the Common Denominator

The common denominator between (x+2) and (x(x+2)) is (x(x+2)).

### Step 3: Rewrite the Fractions with the Common Denominator

To rewrite the fractions with the common denominator (x(x+2)):

- Multiply the first fraction by to make its denominator match the common denominator:
- The second fraction already has the correct denominator, so it remains unchanged:

### Step 4: Subtract the Fractions

Now, subtract the numerators:

### Step 5: Simplify the Numerator

Simplify the expression in the numerator:

## Final Answer

Therefore, the simplified form of the expression is:

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