how do i solve this equation?

2/(x+1)=1/(x-1) - (1/(2x-1))


Get a common denominator (x+1)(x-1)(2x-1)

then, each term, multipy it out.

Gather terms, solve.

To solve the given equation: 2/(x+1) = 1/(x-1) - 1/(2x-1), follow these steps:

Step 1: Obtain a common denominator.
Multiply each term of the equation by the denominator (x+1)(x-1)(2x-1). This will eliminate the denominators and allow you to simplify the equation.

Step 2: Multiply out each term.
Distribute the denominator to each term of the equation. This involves multiplying each term by the corresponding factor from the denominator.

The equation will then become:
2 * (x-1) * (2x-1) = (x+1) * (2x-1) - (x+1) * (x-1)

Step 3: Simplify the equation.
Perform the multiplication and simplify the equation by combining like terms. This involves expanding the products on both sides of the equation and collecting similar terms:

2(2x^2 - 3x + 1) = (x^2 + x - 1) - (x^2 - 1)

This simplifies to:
4x^2 - 6x + 2 = x^2 + x - 1 - x^2 + 1

Step 4: Gather like terms.
Combine the like terms on both sides of the equation:

4x^2 - 6x + 2 = x^2 + x - x^2 + 1 - 1

Simplify further:
4x^2 - 6x + 2 = x

Step 5: Solve for x.
Now that the equation is simplified, you can solve for x. Rearrange the equation so that all terms are on one side and set it equal to zero:

4x^2 - 7x + 2 = 0

Step 6: Factor or use the quadratic formula.
Factor the quadratic equation or use the quadratic formula to find the values of x that satisfy the equation. If the equation does not factor easily, you can use the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

Plug in the values of a, b, and c from the quadratic equation to find the solutions for x.

These steps should help you solve the given equation. Remember, it is crucial to double-check your solutions by substituting them back into the original equation to ensure they satisfy it.