**Finding the Quotient****Problem:**Find the quotient \( \frac{\frac{x + 2}{x^2 - 5x + 6}}{\frac{x + 2}{x^2 - 4x + 3}} \).**Choices:**1. \( \frac{x + 2}{x - 1}, \, x \neq 1, \, x \neq 3 \)2. \( \frac{x - 1}{x - 2}, \, x \neq 2 \)3. \( \frac{x + 2}{x - 2}, \, x \neq -2, \, x \neq 2 \)4. \( \frac{x - 1}{x - 2}, \, x \neq 1, \, x \neq 3 \)**Explanation:**To find the quotient of the given expressions, we need to divide the first fraction by the second fraction.Given expressions:\[ \frac{x + 2}{x^2 - 5x + 6} \]\[ \frac{x + 2}{x^2 - 4x + 3} \]Step 1: Factor the denominators.\[ x^2 - 5x + 6 = (x - 2)(x - 3) \]\[ x^2 - 4x + 3 = (x - 1)(x - 3) \]Step 2: Rewrite the expression with the factored denominators.\[ \frac{x + 2}{(x - 2)(x - 3)} \div \frac{x + 2}{(x - 1)(x - 3)} \]Step 3: Perform the division by multiplying by the reciprocal.\[ \frac{x + 2}{(x - 2)(x - 3)} \times \frac{(x - 1)(x - 3)}{x + 2} \]Step 4: Simplify the expression by canceling common terms.\[ \frac{(x + 2) \cdot (x - 1)(x - 3)}{(x - 2)(x - 3) \cdot (x + 2)} \]Cancel common factors \(x + 2\) and \(x - 3\).\[ \frac

Name: **Finding the Quotient****Problem:**Find the quotient \( \frac{\frac{
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: **Finding the Quotient****Problem:**Find the quotient \( \frac{\frac{x + 2}{x^2 - 5x + 6}}{\frac{x + 2}{x^2 - 4x + 3}} \).**Choices:**1. \( \frac{x + 2}{x - 1}, \, x \neq 1, \, x \neq 3 \)2. \( \frac{x - 1}{x - 2}, \, x \neq 2 \)3. \( \frac{x + 2}{x