Respuesta :
Answer:
B) False
Step-by-step explanation:
A fraction with a zero denominator is undefined in mathematics. Division by zero is not allowed, and it leads to an undefined result.
Final answer:
The claim that a fraction can have a zero denominator at any point in the problem is false. A zero denominator signifies an undefined operation within mathematics, and any fraction with a zero denominator in an equation means the expression is undefined or needs limits analysis in calculus.
Explanation:
The statement questioning whether any fraction can have a zero denominator at any point in the problem is false. A fraction with a zero denominator is not defined because division by zero is an operation that does not have a meaning attached to it within the realm of real numbers. Certain mathematical expressions can lead to a zero denominator, but this typically indicates that the expression is either undefined or needs to be approached with limits, especially in calculus. For instance, the indeterminate form 0/0 does not provide enough information to determine a unique value for a variable.
When solving equations, any operations we perform are valid as long as they maintain equality; this includes scaling both sides by the same non-zero factor or adding and subtracting the same value from both sides. However, one must never multiply or divide by zero to try to solve an equation. Any fraction that has the same non-zero quantity in the numerator and the denominator indeed has a value of 1, since dividing a number by itself yields 1.
In mathematics, particularly calculus, we encounter something known as indeterminate forms. These are expressions that cannot be directly evaluated and require a deeper understanding of limits to analyze. The notion that division by zero could sometimes mean something other than undefined is a misconception. Whether in simple arithmetic or complex calculus, a zero denominator signifies that the expression is not defined or that a limit must be taken to understand its behavior. In physics and economics, expressions that involve divisions by quantities approaching zero are often handled with careful consideration of limits, rather than literal division by zero.
