Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![**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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1b60b83-5432-4bb9-ab52-5e1b6f74cdb9%2F902d4dc4-271b-47aa-a762-5a69c75aaca4%2Fml3qjml_processed.jpeg&w=3840&q=75)
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