Solving the Equation 2/x - 1/x 4: A Step-by-Step Guide

When dealing with algebraic equations involving fractions, it's important to understand how to manipulate the equation to find the value of the unknown variable. In this article, we will explore the solution process for the equation 2/x - 1/x 4. This is a common type of problem in algebra that requires understanding of fraction arithmetic and basic algebraic manipulations.

Understanding the Equation

Let's start with the given equation:

2/x - 1/x 4

We can observe that both fractions have the same denominator, which simplifies the process of solving the equation.

Step-by-Step Solution

Step 1: Combine the Fractions

Since the denominators are the same, we can combine the numerators:

(2 - 1)/x 4

This simplifies to:

1/x 4

Step 2: Solve for x

To solve for x, we need to get rid of the fraction by multiplying both sides of the equation by x:

1 4x

Now, to isolate x, we divide both sides by 4:

x 1/4

Thus, the solution to the equation 2/x - 1/x 4 is x 1/4.

Alternative Approaches

There are multiple ways to solve the equation. Here are a couple of alternative methods:

Method 1: Cross-Multiplication

One can also use cross-multiplication to solve the equation:

2/x - 1/x 4

Can be rewritten as:

(2 - 1)/x 4

After simplifying:

1/x 4

At this point, find x by multiplying both sides by x and then dividing both sides by 4:

x 1/4

Method 2: Factoring and Simplification

The equation can also be solved by factoring out the common fraction:

1/x * (2 - 1) 4

Simplifying this, we get:

1/x * 1 4

Which leads us to:

1/x 4

Isolating x, we find:

x 1/4

Conclusion

The solution to the equation 2/x - 1/x 4 is x 1/4. Understanding the underlying principles and practicing these methods can help in solving similar algebraic problems efficiently.

Related Information

To further enhance your understanding, consider exploring more complex algebraic equations, such as those involving quadratics or higher-degree polynomials. Additionally, practicing with different types of fractions and equations can significantly improve your problem-solving skills.