If 1x - 1y = 1z, then z equals:

1x-1y=1z yxy-xxy=1z y-xxy=1z 1y-xxy=11z xyy-x=z The answer is therefore xyy - x.

smc

algebra intermediate

Problem

\frac{1}{x} - \frac{1}{y} = \frac{1}{z}

, then

z

equals:

(A)

y - x

(B)

x - y

(C)

\frac{y - x}{x y}

(D)

\frac{x y}{y - x}

Solution

\frac{1}{x} - \frac{1}{y} = \frac{1}{z}

\frac{y}{x y} - \frac{x}{x y} = \frac{1}{z}

\frac{y - x}{x y} = \frac{1}{z}

\frac{1}{\frac{y - x}{x y}} = \frac{1}{\frac{1}{z}}

\frac{x y}{y - x} = z

The answer is therefore

\frac{x y}{y - x}

Final answer