\text{Solve for }x of (2x)/(x+1)=(2x-1)/x

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

Evaluate

\frac{2 x}{( x + 1 )} = \frac{( 2 x - 1 )}{x}

Find the domain

More Steps

\frac{2 x}{( x + 1 )} = \frac{( 2 x - 1 )}{x}, x \in (- \infty, - 1) \cup (- 1, 0) \cup (0, + \infty)

Remove the parentheses

\frac{2 x}{x + 1} = \frac{2 x - 1}{x}

Cross multiply

2 x \times x = (x + 1) (2 x - 1)

Simplify the equation

2 x^{2} = (x + 1) (2 x - 1)

Expand the expression

More Steps

2 x^{2} = 2 x^{2} + x - 1

Cancel equal terms on both sides of the expression

0 = x - 1

Swap the sides of the equation

x - 1 = 0

Move the constant to the right side

x = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

x = 1

Check if the solution is in the defined range

x = 1, x \in (- \infty, - 1) \cup (- 1, 0) \cup (0, + \infty)

Solution

x = 1