Your expression is:

\[
\frac{x^2 + x}{5} \times \frac{25}{xy + y}
\]

Let's break it down:

1. The left part is \(\frac{x^2 + x}{5}\), which can be factored as \(\frac{x(x+1)}{5}\).
   
2. The right part is \(\frac{25}{xy + y}\), which can be factored as \(\frac{25}{y(x+1)}\).

Now, multiplying the two parts together:

\[
\frac{x(x+1)}{5} \times \frac{25}{y(x+1)}
\]

You can cancel out the \((x+1)\) terms in the numerator and denominator:

\[
\frac{x}{5} \times \frac{25}{y} = \frac{25x}{5y}
\]

Simplifying:

\[
\frac{25x}{5y} = \frac{5x}{y}
\]

So, the simplified expression is:

\[
\frac{5x}{y}
\]

### Do you need more details or have any questions?

Here are 5 related questions:
1. What if \(x+1\) couldn't be canceled in the expression?
2. How does factoring simplify complex expressions?
3. What is the effect of multiplying two rational expressions?
4. Can this process be extended to higher-degree polynomials?
5. How does canceling terms impact the final result?

**Tip:** Always check for common factors when simplifying expressions!

Learn how to simplify the rational expression x^2 + x / 5 x 25 / xy + y. This step-by-step solution covers key algebraic concepts like factoring, multiplying rational expressions, and canceling common terms. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation