x^2 - 12x +20 /x-2

Answer 1

To simplify the expression $\frac{x^2-12x+20}{x-2}$, let's first factor the quadratic in the numerator.

The quadratic $x^2-12x+20$ can be factored by looking for two numbers that multiply to $20$ and add up to $-12$. The numbers $-10$ and $-2$ fit this requirement. Thus, we can write:

$$x^2-12x+20=(x-10)(x-2)$$

Now we can rewrite the original expression:

$$\frac{x^2-12x+20}{x-2}=\frac{(x-10)(x-2)}{x-2}$$

Assuming $x\ne 2$ (since dividing by zero is not allowed), we can simplify:

$$\frac{(x-10)(x-2)}{x-2}=x-10$$

Therefore, the simplified expression is:

$$x-10\text{for }x\ne 2$$