Solving the Equation 1/x - 2 + 2x - 1 = 6/x by Factorization
In this article, we will solve the equation 1/x - 2 + 2x - 1 = 6/x using the method of factorization.
Given Equation:
1/x - 2 + 2x - 1 = 6/x
Step 1: Multiply both sides by x
To eliminate the fraction, we multiply both sides of the equation by x, which gives us:
1 - 2x + 2x^2 - x = 6
Step 2: Simplify the equation
Simplifying the equation, we get:
2x^2 - 3x - 5 = 0
Step 3: Factorize the equation
Factorizing the quadratic equation, we get:
(2x + 1)(x - 5) = 0
Step 4: Solve for x
Equating each factor to zero, we get:
2x + 1 = 0 --> 2x = -1 --> x = -1/2
x - 5 = 0 --> x = 5
Therefore, the solutions to the equation are x = -1/2 and x = 5.
Conclusion
In this article, we have successfully solved the equation 1/x - 2 + 2x - 1 = 6/x using the method of factorization. The solutions to the equation are x = -1/2 and x = 5.
