Math Problem Statement

x2-9/x+4/x+3/x-5

Solution

It looks like you've written an expression that involves fractions. To clarify, is this the correct interpretation of your expression?

x29x+4x+3x5\frac{x^2 - 9}{x} + \frac{4}{x} + \frac{3}{x} - 5

If so, here's how to simplify it:

  1. Combine like terms with the common denominator xx.
  2. Simplify the resulting expression.

Step 1: Combine the Fractions

All the terms except 5-5 have xx in the denominator. We can write the expression as:

x29+4+3x5\frac{x^2 - 9 + 4 + 3}{x} - 5

Simplify the numerator:

x29+7x5\frac{x^2 - 9 + 7}{x} - 5

Step 2: Factorize the Numerator

The numerator can be factorized if possible. However, in this case:

x29+7=x22x^2 - 9 + 7 = x^2 - 2

So the expression becomes:

x22x5\frac{x^2 - 2}{x} - 5

Step 3: Simplify Further

You can split the fraction:

x2x2x5=x2x5\frac{x^2}{x} - \frac{2}{x} - 5 = x - \frac{2}{x} - 5

So, the simplified expression is:

x2x5x - \frac{2}{x} - 5

This is the simplified form of the given expression.


Do you need any more details or have any questions?

Here are 5 questions related to this simplification:

  1. How would you find the domain of the simplified expression?
  2. What are the possible values of xx where the expression is undefined?
  3. Can you factor x22x^2 - 2 differently for more simplification?
  4. How would you plot this expression on a graph?
  5. What happens to the expression as xx approaches 0?

Tip: Always double-check for common factors before simplifying expressions to make sure you're not missing any potential simplifications.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Fractions
Simplification
Algebra

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12