Understanding the Product Rule: Common Factor Simplification Confusion Explained

Click For Summary
SUMMARY

The discussion centers on the application of the Product Rule in algebra, specifically regarding the simplification of expressions involving common factors. The user questions why one instance of the common factor, x²(x+1), disappears from the numerator after simplification. The confusion arises from the application of the rule where both sides of an equation are multiplied by the common factor, leading to the cancellation of terms. The resolution lies in understanding that only one instance of the common factor is necessary for simplification, which is a standard practice in algebraic manipulation.

PREREQUISITES
  • Understanding of algebraic expressions and equations
  • Familiarity with the Product Rule in calculus
  • Knowledge of common factor simplification techniques
  • Basic skills in manipulating fractions and rational expressions
NEXT STEPS
  • Study the Product Rule in calculus for deeper insights
  • Practice simplifying algebraic fractions with common factors
  • Explore examples of algebraic manipulation involving rational expressions
  • Learn about the concept of cancellation in algebraic equations
USEFUL FOR

Students learning algebra, educators teaching mathematical concepts, and anyone seeking to clarify their understanding of the Product Rule and simplification techniques in algebra.

fitz_calc
Messages
41
Reaction score
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!
 
Physics news on Phys.org
Because the two terms in []'s on the first line are combined into a single [] on the second line.
 

Similar threads

Find Values of Osculating Circle Tangent to a Parabola
  • · Replies 4 ·
Replies
4
Views
2K
Derivative of two polynomials, one of them being squared
  • · Replies 18 ·
Replies
18
Views
2K
How Do You Integrate (x^2+x)/(x^2+x+1) from 0 to 1?
  • · Replies 14 ·
Replies
14
Views
2K
Find derivative of: (3 - x^2)/(4 + x^2); Quotient Rule vs. Product Rule
  • · Replies 6 ·
Replies
6
Views
3K
What is the Factored Form of the Derivative Using Product Rule?
  • · Replies 2 ·
Replies
2
Views
2K
Differentiation - Product Rule
  • · Replies 3 ·
Replies
3
Views
2K
Derivative Help: differentiate using product rule
  • · Replies 1 ·
Replies
1
Views
2K
Solve ##\dfrac{3x-6}{5-x}+\dfrac{11-2x}{10-4x}=3\dfrac{1}{2}##
  • · Replies 3 ·
Replies
3
Views
2K
Calculus Confusion over Calculus Book example footnote
  • · Replies 9 ·
Replies
9
Views
3K
Finding f'(x) for Logarithm Derivatives Homework with Product and Quotient Rules
  • · Replies 3 ·
Replies
3
Views
2K