Question

Simplify completely.x2−4x+3x2−9⋅x+3x−1(1 point)Responsesx−3x−1the fraction with numerator x minus 3 and denominator x minus 1x−1x−3the fraction with numerator x minus 1 and denominator x minus 311x+3x−3the fraction with numerator x plus 3 and denominator x minus 3

Answer 1

To simplify the expression \(\frac{x^2 - 4x + 3}{x^2 - 9} \cdot \frac{x + 3}{x - 1}\), we will first factor the polynomials in the numerator and denominator.

1. Factor \(x^2 - 4x + 3\):
\[
x^2 - 4x + 3 = (x - 1)(x - 3)
\]

2. Factor \(x^2 - 9\):
\[
x^2 - 9 = (x - 3)(x + 3)
\]

Now, we can rewrite the expression with the factored forms:
\[
\frac{(x - 1)(x - 3)}{(x - 3)(x + 3)} \cdot \frac{x + 3}{x - 1}
\]

Next, we multiply the fractions:
\[
\frac{(x - 1)(x - 3)(x + 3)}{(x - 3)(x + 3)(x - 1)}
\]

Now we can cancel the common factors in the numerator and the denominator:
- \((x - 1)\) cancels with \((x - 1)\)
- \((x + 3)\) cancels with \((x + 3)\)
- \((x - 3)\) cancels with \((x - 3)\)

After canceling out all common factors, we are left with:
\[
1
\]

Therefore, the completely simplified form of the given expression is:
\[
\boxed{1}
\]