We can see that the function approaches a particular
value as *x* approaches `3` from the left:

x |
2.5 | 2.6 | 2.7 | 2.8 | 2.9 |

f(x) |
3.5 | 3.6 | 3.7 | 3.8 | 3.9 |

Continuing, we get closer and closer to `x = 3`:

x |
2.9 | 2.92 | 2.94 | 2.96 | 2.97 | 2.98 | 2.99 |

f(x) |
3.9 | 3.92 | 3.94 | 3.96 | 3.97 | 3.98 | 3.99 |

Likewise, approaching `x = 3` from the right gives the same limit value:

x |
3.5 | 3.1 | 3.01 | 3.00001 |

f(x) |
4.5 | 4.1 | 4.01 | 4.00001 |

We note that the function value is getting closer and closer to `4`.

We write:

`lim_(xrarr3)(x^2-2x-3)/(x-3)=4`

**NOTE:** We could have evaluated this limit by **factoring** first:

`lim_(xrarr3)(x^2-2x-3)/(x-3)`

`=lim_(xrarr3)((x+1)(x-3))/(x-3)`

`=lim_(xrarr3)(x+1)`

`=4`