To simplify the expression, we can use long division.

First, divide n^2 by n to get n. Write this above the division line.

```
n
-----------
n + 1 | n^2 + 2n - 3
```

Next, multiply n + 1 by n to get n^2 + n. Write this below the n^2 + 2n - 3.

```
n
-----------
n + 1 | n^2 + 2n - 3
- (n^2 + n)
```

Subtract n^2 + n from n^2 + 2n to get n. Write this below the line.

```
n
-----------
n + 1 | n^2 + 2n - 3
- (n^2 + n)
--------
n
```

Next, bring down the -3.

```
n
-----------
n + 1 | n^2 + 2n - 3
- (n^2 + n)
--------
n - 3
```

Finally, divide n - 3 by n + 1 to get 1. Write this above the line.

```
n + 1
-----------
n + 1 | n^2 + 2n - 3
- (n^2 + n)
--------
n - 3
- (n - 3)
```

Subtract n - 3 from n - 3 to get 0. Write this below the line.

```
n + 1
-----------
n + 1 | n^2 + 2n - 3
- (n^2 + n)
--------
n - 3
- (n - 3)
--------
0
```

Therefore, the simplified expression is 1.