Solving the Equation: 2/x + 2 - 1/x + 1 = 4/x + 4 - 3/x + 3
In this article, we will solve the given equation step by step.
The Equation
The equation is:
$\frac{2}{x} + 2 - \frac{1}{x} + 1 = \frac{4}{x} + 4 - \frac{3}{x} + 3$
Step 1: Combine Like Terms
First, we will combine the like terms on the left-hand side of the equation:
$\frac{2}{x} - \frac{1}{x} + 2 + 1 = \frac{1}{x} + 3$
Step 2: Combine Like Terms (again)
Now, we will combine the like terms on the right-hand side of the equation:
$\frac{4}{x} - \frac{3}{x} + 4 + 3 = \frac{1}{x} + 7$
Step 3: Equate the Two Expressions
Now, we can equate the two expressions:
$\frac{1}{x} + 3 = \frac{1}{x} + 7$
Step 4: Solve for x
Subtract 3 from both sides of the equation:
$\frac{1}{x} = \frac{1}{x} + 4$
Subtract $\frac{1}{x}$ from both sides:
$0 = 4$
This is a contradiction, which means that there is no value of x that satisfies the equation.
Conclusion
Therefore, the equation $\frac{2}{x} + 2 - \frac{1}{x} + 1 = \frac{4}{x} + 4 - \frac{3}{x} + 3$ has no solution.
