Express each of the following as a rational expressions.`(x^2-5x+6)/(x^2-9x+20) div( x^2-3x+2)/(x^2-5x+4)`:

Options

A. `(x-4)/(x-3)`
B. `(x-3)/(x-5)`
C. `(x-2)/(x-5)`
D. `(x-5)/(x-3)`

Answer

To express the given expression \(\frac{x^2 - 5x + 6}{x^2 - 9x + 20} \div \frac{x^2 - 3x + 2}{x^2 - 5x + 4}\) as a rational expression, we will follow these steps:

### Step 1: Rewrite the Division as Multiplication
The division of fractions can be rewritten as multiplication by the reciprocal. Therefore, we can rewrite the expression as:
\[ \frac{x^2 - 5x + 6}{x^2 - 9x + 20} \times \frac{x^2 - 5x + 4}{x^2 - 3x + 2} \]