Solve 1/x-1/y=1/ztext{find}xtext{given}y=5text{and}z=2

$$\frac { 1 } { x } - \frac { 1 } { y } = \frac { 1 } { z } \text { find } x \text { given } y = 5 \text { and } z = 2$$

Solve for x, y, z

$$x = \frac{10}{7} = 1\frac{3}{7} \approx 1.428571429$$

$$y=5$$

$$z=2$$

Solution Steps

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

$$\frac{1}{x}-\frac{1}{5}=\frac{1}{2}$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10x, the least common multiple of x,5,2.

$$10-2x=5x$$

Subtract 5x from both sides.

$$10-2x-5x=0$$

Combine -2x and -5x to get -7x.

$$10-7x=0$$

Subtract 10 from both sides. Anything subtracted from zero gives its negation.

$$-7x=-10$$

Divide both sides by -7.

$$x=\frac{-10}{-7}$$

Fraction \frac{-10}{-7} can be simplified to \frac{10}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{10}{7}$$

The system is now solved.

$$x=\frac{10}{7} y=5 z=2$$