Solve 1/z+1/3+1/14

$$\frac { 1 } { z } + \frac { 1 } { 3 } + \frac { 1 } { 14 }$$

Evaluate

$$\frac{17}{42}+\frac{1}{z}$$

Solution Steps

Least common multiple of 3 and 14 is 42. Convert \frac{1}{3} and \frac{1}{14} to fractions with denominator 42.

$$\frac{1}{z}+\frac{14}{42}+\frac{3}{42}$$

Since \frac{14}{42} and \frac{3}{42} have the same denominator, add them by adding their numerators.

$$\frac{1}{z}+\frac{14+3}{42}$$

Add 14 and 3 to get 17.

$$\frac{1}{z}+\frac{17}{42}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z and 42 is 42z. Multiply \frac{1}{z} times \frac{42}{42}. Multiply \frac{17}{42} times \frac{z}{z}.

$$\frac{42}{42z}+\frac{17z}{42z}$$

Since \frac{42}{42z} and \frac{17z}{42z} have the same denominator, add them by adding their numerators.

$$\frac{42+17z}{42z}$$

Factor

$$\frac{17z+42}{42z}$$