Understanding the Product Rule: Common Factor Simplification Confusion Explained

In summary, the question is about a simplification method using a common factor and why one of the terms disappears from the numerator in the final answer. The answer is that the two terms in brackets were combined into one term, resulting in only one numerator being used in the final calculation.
  • #1
fitz_calc
41
0
I've already done the problem (here is the last part, sorry for crappy pic)

Picture002.jpg


My question; if I multiply both sides of the + by x^2(x+1) / x^2(x+1) as the common factor to simplify the equation, then why does on of the x^2(x+1) disappear from the numerator in the final answer? It appears as though both denominators were used to simplify both sides of the +, yet only one numerator was used in the final calculation. Please tell me I'm not going crazy!
 
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  • #2
Because the two terms in []'s on the first line are combined into a single [] on the second line.
 

1. What is the product rule in mathematics?

The product rule is a mathematical rule used to simplify the multiplication of two terms with the same variable base. It states that when multiplying two terms with the same base, you can add their exponents to simplify the expression.

2. How is the product rule related to common factor simplification?

The product rule is closely related to common factor simplification because it is used to simplify expressions with common factors. By applying the product rule, you can combine like terms and eliminate common factors, making the expression easier to solve.

3. Why do students often get confused with the product rule and common factor simplification?

Students often get confused with the product rule and common factor simplification because they both involve simplifying expressions with variables. Additionally, they may not fully understand the concept of exponents and how they relate to multiplication and division.

4. How can I remember the product rule?

A helpful way to remember the product rule is to think of it as "add the exponents, keep the base." This means that when multiplying two terms with the same base, you add the exponents and keep the base the same in the simplified expression.

5. Can the product rule be applied to expressions with more than two terms?

Yes, the product rule can be applied to expressions with more than two terms. However, it is important to first simplify any common factors before applying the product rule. Once the expression is simplified, the product rule can be used to simplify further if there are still terms with the same base.

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