Let's solve the given mathematical expression:

\[
4 - \frac{1}{x^2} \div 2 - \frac{1}{x}
\]

To solve this expression, we should follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step 1: Simplify the Division
First, let's handle the division part \(\frac{1}{x^2} \div 2\). Dividing by 2 is equivalent to multiplying by \(\frac{1}{2}\):

\[
\frac{1}{x^2} \div 2 = \frac{1}{x^2} \times \frac{1}{2} = \frac{1}{2x^2}
\]

### Step 2: Substitute Back into the Expression
Now substitute this result back into the original expression:

\[
4 - \frac{1}{2x^2} - \frac{1}{x}
\]

### Step 3: Combine Terms
There are no like terms that can be combined here since each term has a different denominator. Therefore, the expression, in its simplest form, is:

\[
4 - \frac{1}{2x^2} - \frac{1}{x}
\]

This is the simplified version of the given expression.

### Summary
\[
4 - \frac{1}{x^2} \div 2 - \frac{1}{x} = 4 - \frac{1}{2x^2} - \frac{1}{x}
\]

Would you like to know more about this topic, or do you have any questions?

### Follow-up Questions:

1. How would you solve this expression if there were parentheses indicating a different order of operations?
2. What happens to the expression if \( x = 0 \)?
3. How would you graph the function \( f(x) = 4 - \frac{1}{2x^2} - \frac{1}{x} \)?
4. Can this expression be rewritten in terms of a common denominator?
5. How would this expression change if the division sign were replaced with a multiplication sign?

### Tip:
When solving algebraic expressions, always look for ways to factorize and simplify terms to make calculations easier and to understand the relationships between different components of the expression.

Learn how to simplify the expression 4 - 1/x^2 / 2 - 1/x step-by-step with this detailed solution. Understand the order of operations (PEMDAS), division of fractions, and simplification techniques in algebraic expressions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation