Question

X*x-16         x*x-6x+9 ---------- * ------------------ x-3                  2x-8

Answer 1

$\frac{(x - 4)(x + 4)}{(x - 3)} \times \frac{ {(x - 3)}^{2} }{2(x - 4)} = \frac{(x + 4)(x - 3)}{2}$

Answer 2

To simplify the expression $\frac{{x^2 - 16}}{{x - 3}} \cdot \frac{{x^2 - 6x + 9}}{{2x - 8}},$ you can first factor the quadratic expressions in both numerators and denominators and then simplify further. Here's how you can do it step by step:

1. Factor each expression:

   • $x^2 - 16$ factors to $(x + 4)(x - 4)$.
   • $x^2 - 6x + 9$ factors to $(x - 3)(x - 3)$.
   • $x - 3$ is already in factored form.
   • $2x - 8$ factors to $2(x - 4)$.

2. Rewrite the expression with the factored forms: $\frac{{(x + 4)(x - 4)}}{{x - 3}} \cdot \frac{{(x - 3)(x - 3)}}{{2(x - 4)}}$

3. Cancel out common factors in the numerators and denominators:

   • $x - 4$ in the first fraction cancels out with $x - 4$ in the second fraction.
   • $x - 3$ in the second fraction cancels out with $x - 3$ in the first fraction.

After canceling out the common factors, you are left with: $\frac{{(x + 4) \cdot (x - 3)}}{{2}}$

So, the simplified expression is $\frac{{(x + 4)(x - 3)}}{2}$.