Mathias Found The Product 4 X + 8 X ⋅ 5 X + 2 \frac{4x+8}{x} \cdot \frac{5}{x+2} X 4 X + 8 ​ ⋅ X + 2 5 ​ As Follows: 4 X + 8 X ⋅ 5 X + 2 = 4 X + 8 X ⋅ 5 X + 2 = 12 1 ⋅ 5 X + 2 = 60 X + 2 \frac{4x+8}{x} \cdot \frac{5}{x+2} = \frac{4x+8}{x} \cdot \frac{5}{x+2} = \frac{12}{1} \cdot \frac{5}{x+2} = \frac{60}{x+2} X 4 X + 8 ​ ⋅ X + 2 5 ​ = X 4 X + 8 ​ ⋅ X + 2 5 ​ = 1 12 ​ ⋅ X + 2 5 ​ = X + 2 60 ​ Which Of The Following Best

Introduction

Mathias has encountered a complex product of two fractions, $\frac{4x+8}{x} \cdot \frac{5}{x+2}$, and has attempted to simplify it. However, his solution seems to be incorrect. In this article, we will re-examine Mathias' work and provide a step-by-step analysis to determine the correct simplification of the given product.

Mathias' Solution

Mathias' solution is as follows:

$$\frac{4x+8}{x} \cdot \frac{5}{x+2} = \frac{4x+8}{x} \cdot \frac{5}{x+2} = \frac{12}{1} \cdot \frac{5}{x+2} = \frac{60}{x+2}$$

Step 1: Factor the Numerator

The first step in simplifying the product is to factor the numerator of the first fraction. We can rewrite $4x+8$ as $4(x+2)$.

$$\frac{4x+8}{x} \cdot \frac{5}{x+2} = \frac{4(x+2)}{x} \cdot \frac{5}{x+2}$$

Step 2: Cancel Common Factors

Now that we have factored the numerator, we can cancel common factors between the two fractions. The common factor between $4(x+2)$ and $x+2$ is $x+2$. We can cancel this factor to simplify the expression.

$$\frac{4(x+2)}{x} \cdot \frac{5}{x+2} = \frac{4}{x} \cdot 5$$

Step 3: Multiply the Numerators

Now that we have simplified the expression, we can multiply the numerators to get the final result.

$$\frac{4}{x} \cdot 5 = \frac{20}{x}$$

Conclusion

In conclusion, Mathias' solution was incorrect. The correct simplification of the product $\frac{4x+8}{x} \cdot \frac{5}{x+2}$ is $\frac{20}{x}$. We were able to simplify the expression by factoring the numerator, canceling common factors, and multiplying the numerators.

Common Mistakes

There are several common mistakes that Mathias made in his solution. Firstly, he failed to factor the numerator, which led to an incorrect simplification. Secondly, he failed to cancel common factors, which also led to an incorrect simplification. Finally, he failed to multiply the numerators, which resulted in an incorrect final answer.

Tips for Simplifying Products

When simplifying products of fractions, there are several tips that can be helpful. Firstly, always factor the numerators to simplify the expression. Secondly, cancel common factors between the two fractions to simplify the expression. Finally, multiply the numerators to get the final result.

Conclusion

In conclusion, Mathias' solution was incorrect. The correct simplification of the product $\frac{4x+8}{x} \cdot \frac{5}{x+2}$ is $\frac{20}{x}$. We were able to simplify the expression by factoring the numerator, canceling common factors, and multiplying the numerators. By following these steps, we can ensure that we get the correct simplification of products of fractions.

Final Answer

$$

Introduction

In our previous article, we analyzed Mathias' attempt to simplify the product $\frac{4x+8}{x} \cdot \frac{5}{x+2}$ and provided a step-by-step solution to determine the correct simplification. In this article, we will provide a Q&A section to address common questions and concerns related to simplifying products of fractions.

Q&A

Q: What is the first step in simplifying a product of fractions?

A: The first step in simplifying a product of fractions is to factor the numerators to simplify the expression.

Q: How do I factor the numerators?

A: To factor the numerators, look for common factors between the terms. In the case of $4x+8$, we can rewrite it as $4(x+2)$.

Q: What is the next step after factoring the numerators?

A: After factoring the numerators, cancel common factors between the two fractions to simplify the expression.

Q: How do I cancel common factors?

A: To cancel common factors, look for common factors between the numerators and denominators of the two fractions. In the case of $\frac{4(x+2)}{x} \cdot \frac{5}{x+2}$, we can cancel the common factor of $x+2$.

Q: What is the final step in simplifying a product of fractions?

A: The final step in simplifying a product of fractions is to multiply the numerators to get the final result.

Q: What are some common mistakes to avoid when simplifying products of fractions?

A: Some common mistakes to avoid when simplifying products of fractions include failing to factor the numerators, failing to cancel common factors, and failing to multiply the numerators.

Q: How can I ensure that I get the correct simplification of a product of fractions?

A: To ensure that you get the correct simplification of a product of fractions, follow these steps:

1. Factor the numerators to simplify the expression.
2. Cancel common factors between the two fractions to simplify the expression.
3. Multiply the numerators to get the final result.

Q: What are some tips for simplifying products of fractions?

A: Some tips for simplifying products of fractions include:

• Always factor the numerators to simplify the expression.
• Cancel common factors between the two fractions to simplify the expression.
• Multiply the numerators to get the final result.

Q: Can you provide an example of a product of fractions that can be simplified using these steps?

A: Yes, consider the product $\frac{3x+6}{x} \cdot \frac{2}{x+2}$. We can factor the numerators to get $\frac{3(x+2)}{x} \cdot \frac{2}{x+2}$. We can then cancel the common factor of $x+2$ to get $\frac{3}{x} \cdot 2$. Finally, we can multiply the numerators to get $\frac{6}{x}$.

Conclusion

In conclusion, simplifying products of fractions requires careful attention to detail and a step-by-step approach. By following these steps and avoiding common mistakes, you can ensure that you get the correct simplification of a product of fractions. Remember to factor the numerators, cancel common factors, and multiply the numerators to get the final result.

Final Answer

The final answer is $\boxed{\frac{6}{x}}$.