Let's simplify the given expression step by step:

The expression is:

\[
\frac{2}{5a+4} \times \frac{45a + 36}{a}
\]

### Step 1: Simplify the second fraction

Factor out the common factor in the numerator of the second fraction:

\[
45a + 36 = 9(5a + 4)
\]

So the expression becomes:

\[
\frac{2}{5a+4} \times \frac{9(5a+4)}{a}
\]

### Step 2: Cancel out common terms

Since \(5a+4\) appears in both the numerator and the denominator, we can cancel it out:

\[
\frac{2}{\cancel{5a+4}} \times \frac{9\cancel{(5a+4)}}{a}
\]

This simplifies to:

\[
\frac{2 \times 9}{a} = \frac{18}{a}
\]

### Final Answer:

\[
\frac{18}{a}
\]

Would you like further details on the steps or have any questions?

Here are 5 related questions to explore:
1. How do you factor polynomials like \(45a + 36\)?
2. What are the steps to simplify complex fractions?
3. How do you handle expressions with variables in both the numerator and denominator?
4. What happens if \(a = 0\) in this expression?
5. How do you simplify algebraic expressions involving multiple terms?

**Tip:** Always look for common factors to simplify expressions quickly.

Learn how to simplify the rational expression 2/(5a+4) x (45a+36)/a by factoring and canceling common terms. This algebraic problem demonstrates factoring techniques and the simplification of fractions with variables. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation