## Simplifying the Rational Expression (x-3)x^2-6x+9 / (x+3)

This article explores the simplification of the rational expression:

**(x-3)x^2-6x+9 / (x+3)**

We will simplify this expression by factoring the numerator and denominator, then canceling out common factors.

### Factoring the Numerator

The numerator, **(x-3)x^2-6x+9**, is a quadratic expression. We can factor it using the following steps:

**Factor out the common factor (x-3):**(x-3) (x^2 - 2x + 3)**Factor the remaining quadratic expression:**(x-3) (x-1)(x-3)

Therefore, the factored form of the numerator is **(x-3)^2 (x-1)**.

### Factoring the Denominator

The denominator, **(x+3)**, is already in its simplest factored form.

### Simplifying the Expression

Now, let's rewrite the original expression with the factored forms:

**(x-3)^2 (x-1) / (x+3)**

We can cancel out the common factor (x-3) from the numerator and denominator, resulting in:

**(x-3)(x-1) / (x+3)**

This is the simplified form of the original expression.

### Important Considerations:

**Restrictions:**Remember that the original expression is undefined when the denominator is zero. Therefore, x ≠ -3.**Domain:**The domain of the simplified expression is all real numbers except x = -3.

In conclusion, the simplified form of the expression (x-3)x^2-6x+9 / (x+3) is **(x-3)(x-1) / (x+3)**, with the restriction x ≠ -3.