Math Problem Statement

(3x/x-3)

Solution

It seems you're working with an expression:

3xx3\frac{3x}{x - 3}

This expression is a rational function, meaning it is a fraction where both the numerator and denominator are polynomials. Let's break it down:

  1. Numerator: 3x3x
  2. Denominator: x3x - 3

Important notes:

  • This expression is undefined if x=3x = 3, since the denominator would become zero, leading to division by zero.
  • For any other values of xx, the expression simplifies as it is.

So, the expression remains:

3xx3,with x3.\frac{3x}{x - 3}, \quad \text{with } x \neq 3.

Would you like more details on how to work with this expression, or do you have any specific questions?

Here are 5 related questions:

  1. What happens when you substitute specific values of xx into this expression?
  2. How do you graph a rational function like 3xx3\frac{3x}{x-3}?
  3. Can you simplify the expression further under certain conditions?
  4. What is the domain of the function 3xx3\frac{3x}{x - 3}?
  5. How does the function behave as xx approaches 3 from either side?

Tip: Always check for points where the denominator becomes zero when working with rational expressions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions

Formulas

Rational function: f(x) = p(x)/q(x)
Domain restrictions: Denominator ≠ 0

Theorems

Undefined points in rational functions

Suitable Grade Level

Grades 9-11