Question

If $\frac{1}{3}+\frac{1}{2}+\frac{1}{x}=4$, then x = ?

(a) $\frac{5}{18}$
(b) $\frac{6}{19}$
(c) $\frac{18}{5}$
(d) $\frac{24}{11}$

Answer 1

(b) $\frac{6}{19}$

$$\begin{gathered} \frac{1}{3}+\frac{1}{2}+\frac{1}{x}=4 \\ \frac{1}{x}=4-\frac{1}{3}-\frac{1}{2} \\ \frac{1}{x}=\frac{4\times 6}{1\times 6}-\frac{1\times 2}{3\times 2}-\frac{1\times 3}{2\times 3}=\frac{24}{6}-\frac{2}{6}-\frac{3}{6} \\ \frac{1}{x}=\frac{24-2-3}{6} \\ \frac{1}{x}=\frac{19}{6} \\ x=\frac{6}{19} \end{gathered}$$