(2x+1)+(3)/(2x+1)=4 X =-(1)/(2)

Jasonbradley

2 min read Jun 16, 2024

Solving the Equation: (2x+1) + (3)/(2x+1) = 4, where x = -1/2

This article explores the process of solving the given equation and analyzing the solution at x = -1/2.

The Equation:

We have the equation: (2x+1) + (3)/(2x+1) = 4

Substitution and Simplification:

Let's substitute x = -1/2 into the equation:

(2(-1/2)+1) + (3)/(2(-1/2)+1) = 4
(-1 + 1) + (3)/( -1 + 1) = 4
0 + (3)/0 = 4

The Problem: Division by Zero

We encounter a problem here: division by zero is undefined. This means that the equation is not solvable at x = -1/2.

Why does this happen?

The denominator (2x+1) becomes zero when x = -1/2. This creates a singularity in the equation, making it undefined at this specific point.

Conclusion:

The equation (2x+1) + (3)/(2x+1) = 4 has no solution at x = -1/2. This is due to the denominator becoming zero at that value, leading to undefined behavior in the equation.