The expression which expression is equivalent to 3x/x+1 divided by x+1 invites us to explore the realm of equivalent expressions, where mathematical equations take on multiple forms while maintaining their fundamental equality. This introductory paragraph sets the stage for an in-depth examination of this intriguing concept, promising a journey of discovery and enlightenment.
As we delve into the intricacies of equivalent expressions, we will unravel the steps involved in simplifying the given expression, revealing its hidden equivalence. Through a series of logical deductions, we will demonstrate how the expression can be transformed into a simpler form, showcasing the power of mathematical manipulation.
Equivalent Expressions for 3x/(x+1) / (x+1): Which Expression Is Equivalent To 3x/x+1 Divided By X+1
This article explores the concept of equivalent expressions and demonstrates how to simplify the expression 3x/(x+1) / (x+1) to its equivalent form.
Equivalent Expressions
Equivalent expressions are mathematical expressions that have the same value for all values of the variables involved. For example, 2x + 1 and x + 3 are equivalent expressions because they both evaluate to the same value for any given value of x.
Simplifying the Expression
To simplify the expression 3x/(x+1) / (x+1), we can apply the following steps:
- Remove the common factor (x+1) from the numerator and denominator:
- Simplify the expression by canceling out the common factor:
3x/(x+1) / (x+1) = 3x/(x+1)- 1/(x+1)
3x/(x+1) – 1/(x+1) = 3x/(x+1)^2
Comparison of Expressions, Which expression is equivalent to 3x/x+1 divided by x+1
The simplified expression 3x/(x+1)^2 is equivalent to the original expression 3x/(x+1) / (x+1) because they both evaluate to the same value for all values of x.
Applications of the Equivalent Expression
The equivalent expression 3x/(x+1)^2 can be used in various mathematical operations, such as:
- Solving equations
- Simplifying algebraic expressions
- Evaluating limits
Popular Questions
What is the purpose of simplifying expressions?
Simplifying expressions helps us to rewrite them in a more concise and manageable form, making it easier to perform mathematical operations and identify patterns.
How can equivalent expressions be used in real-world scenarios?
Equivalent expressions can be used to solve equations, simplify complex calculations, and model real-world phenomena, such as the motion of objects or the growth of populations.
