Now It's Your Turn To Practice Multiplying Rational Expressions. Try To Answer The Question Below.Multiply The Rational Expressions:${ \frac{4}{5x} \cdot \frac{2}{x-1} }$A. { \frac{6}{6x-1}$}$B. { \frac{8}{5x^2-5x}$}$C.

Introduction

Multiplying rational expressions is a fundamental concept in algebra that requires a clear understanding of the rules and procedures involved. In this article, we will delve into the world of rational expressions and explore the process of multiplying them. We will use a specific example to illustrate the steps involved and provide a detailed explanation of each step.

What are Rational Expressions?

Before we dive into the process of multiplying rational expressions, let's first define what rational expressions are. A rational expression is a fraction that contains variables and/or constants in the numerator and/or denominator. Rational expressions can be expressed in the form of:

$$\frac{p(x)}{q(x)}$$

where p(x) and q(x) are polynomials.

The Rules of Multiplying Rational Expressions

When multiplying rational expressions, there are certain rules that we need to follow. These rules are:

1. Multiply the numerators: Multiply the numerators of the two rational expressions.
2. Multiply the denominators: Multiply the denominators of the two rational expressions.
3. Simplify the expression: Simplify the resulting expression by canceling out any common factors.

Example: Multiplying Rational Expressions

Let's use the following example to illustrate the process of multiplying rational expressions:

$$\frac{4}{5x} \cdot \frac{2}{x-1}$$

To multiply these two rational expressions, we need to follow the rules outlined above.

Step 1: Multiply the Numerators

The first step is to multiply the numerators of the two rational expressions. In this case, we have:

$$4 \cdot 2 = 8$$

So, the numerator of the resulting expression is 8.

Step 2: Multiply the Denominators

The next step is to multiply the denominators of the two rational expressions. In this case, we have:

$$5x \cdot (x-1) = 5x^2 - 5x$$

So, the denominator of the resulting expression is $5x^2 - 5x$.

Step 3: Simplify the Expression

The final step is to simplify the resulting expression by canceling out any common factors. In this case, we have:

$$\frac{8}{5x^2 - 5x}$$

There are no common factors to cancel out, so the resulting expression is already simplified.

Conclusion

In this article, we have explored the process of multiplying rational expressions. We have outlined the rules involved and used a specific example to illustrate the steps involved. By following these rules and procedures, you can multiply rational expressions with ease.

Answer

The correct answer is:

$$\frac{8}{5x^2 - 5x}$$

This is option B.

Discussion

Multiplying rational expressions is a fundamental concept in algebra that requires a clear understanding of the rules and procedures involved. In this article, we have explored the process of multiplying rational expressions and provided a detailed explanation of each step. By following these rules and procedures, you can multiply rational expressions with ease.

Practice Problems

Here are some practice problems to help you reinforce your understanding of multiplying rational expressions:

1. Multiply the rational expressions: $\frac{3}{4x} \cdot \frac{2}{x+1}$
2. Multiply the rational expressions: $\frac{5}{6x} \cdot \frac{3}{x-2}$
3. Multiply the rational expressions: $\frac{2}{3x} \cdot \frac{4}{x+2}$

Solutions

Here are the solutions to the practice problems:

1. $\frac{6}{4x^2 + 4x}$
2. $\frac{15}{6x^2 - 12x}$
3. $\frac{8}{9x^2 + 12x}$

Conclusion

Introduction

Multiplying rational expressions is a fundamental concept in algebra that requires a clear understanding of the rules and procedures involved. In our previous article, we explored the process of multiplying rational expressions and provided a detailed explanation of each step. In this article, we will answer some of the most frequently asked questions about multiplying rational expressions.

Q&A

Q: What is the first step in multiplying rational expressions?

A: The first step in multiplying rational expressions is to multiply the numerators of the two rational expressions.

Q: How do I multiply the denominators of two rational expressions?

A: To multiply the denominators of two rational expressions, you need to multiply the factors in the denominators. For example, if you have the rational expressions $\frac{1}{x}$ and $\frac{1}{y}$, the product of the denominators is $xy$.

Q: What is the final step in multiplying rational expressions?

A: The final step in multiplying rational expressions is to simplify the resulting expression by canceling out any common factors.

Q: Can I cancel out any common factors in the numerator and denominator?

A: Yes, you can cancel out any common factors in the numerator and denominator. For example, if you have the rational expression $\frac{6x}{2x}$, you can cancel out the common factor of $2x$ to get $\frac{3}{1}$.

Q: What if I have a rational expression with a negative exponent?

A: If you have a rational expression with a negative exponent, you can rewrite it as a fraction with a positive exponent. For example, if you have the rational expression $x^{-2}$, you can rewrite it as $\frac{1}{x^2}$.

Q: Can I multiply rational expressions with different variables?

A: Yes, you can multiply rational expressions with different variables. For example, if you have the rational expressions $\frac{1}{x}$ and $\frac{1}{y}$, you can multiply them to get $\frac{1}{xy}$.

Q: What if I have a rational expression with a zero denominator?

A: If you have a rational expression with a zero denominator, you cannot simplify it further. For example, if you have the rational expression $\frac{1}{0}$, you cannot simplify it further because the denominator is zero.

Common Mistakes

Mistake 1: Not canceling out common factors

One common mistake when multiplying rational expressions is not canceling out common factors. For example, if you have the rational expression $\frac{6x}{2x}$, you should cancel out the common factor of $2x$ to get $\frac{3}{1}$.

Mistake 2: Not simplifying the expression

Another common mistake when multiplying rational expressions is not simplifying the expression. For example, if you have the rational expression $\frac{6x}{2x}$, you should simplify it to get $\frac{3}{1}$.

Mistake 3: Not following the order of operations

A third common mistake when multiplying rational expressions is not following the order of operations. For example, if you have the rational expressions $\frac{1}{x}$ and $\frac{1}{y}$, you should multiply the numerators and denominators separately before simplifying the expression.

Conclusion

Multiplying rational expressions is a fundamental concept in algebra that requires a clear understanding of the rules and procedures involved. In this article, we have answered some of the most frequently asked questions about multiplying rational expressions and highlighted some common mistakes to avoid. By following these rules and procedures, you can multiply rational expressions with ease.

Practice Problems

Here are some practice problems to help you reinforce your understanding of multiplying rational expressions:

1. Multiply the rational expressions: $\frac{3}{4x} \cdot \frac{2}{x+1}$
2. Multiply the rational expressions: $\frac{5}{6x} \cdot \frac{3}{x-2}$
3. Multiply the rational expressions: $\frac{2}{3x} \cdot \frac{4}{x+2}$

Solutions

Here are the solutions to the practice problems:

1. $\frac{6}{4x^2 + 4x}$
2. $\frac{15}{6x^2 - 12x}$
3. $\frac{8}{9x^2 + 12x}$

Additional Resources

For more information on multiplying rational expressions, you can check out the following resources:

• Khan Academy: Multiplying Rational Expressions
• Mathway: Multiplying Rational Expressions
• Wolfram Alpha: Multiplying Rational Expressions

Conclusion

Multiplying rational expressions is a fundamental concept in algebra that requires a clear understanding of the rules and procedures involved. In this article, we have answered some of the most frequently asked questions about multiplying rational expressions and highlighted some common mistakes to avoid. By following these rules and procedures, you can multiply rational expressions with ease.