Solve {l}{1+1/x=2-2/x}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 1 + \frac{1}{x} = 2 - \frac{2}{x} }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=3$$

Solution Steps

Consider the first equation. Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x+1=x\times 2-2$$

Subtract x\times 2 from both sides.

$$x+1-x\times 2=-2$$

Combine x and -x\times 2 to get -x.

$$-x+1=-2$$

Subtract 1 from both sides.

$$-x=-2-1$$

Subtract 1 from -2 to get -3.

$$-x=-3$$

Divide both sides by -1.

$$x=\frac{-3}{-1}$$

Fraction \frac{-3}{-1} can be simplified to 3 by removing the negative sign from both the numerator and the denominator.

$$x=3$$

Consider the second equation. Insert the known values of variables into the equation.

$$y=3$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=3$$

The system is now solved.

$$x=3 y=3 z=3$$