Solve for x ((2x-1)(x+1))/(x-1)=0

$\frac{(2 x - 1) (x + 1)}{(x - 1)} = 0$

Step 1

Set the numerator equal to zero.

$(2 x - 1) (x + 1) = 0$

Step 2

Solve the equation for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 1 = 0$

$x + 1 = 0$

Set $2 x - 1$ equal to $0$ and solve for $x$ .

Set $2 x - 1$ equal to $0$ .

$2 x - 1 = 0$

Solve $2 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The final solution is all the values that make $(2 x - 1) (x + 1) = 0$ true.

$x = \frac{1}{2}, - 1$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - 1$

Decimal Form:

$x = 0.5, - 1$