$$\left. \begin{array} { l } { \frac { 1 } { a } - \frac { 1 } { b } = \frac { 1 } { 6 } \cdot \frac { 1 } { 4 } } \\ { a = \frac { 1 } { 2 } , 6 } \end{array} \right.$$
$c=6$
$$\frac{1}{\frac{1}{2}}-\frac{1}{b}=\frac{1}{6}\times \frac{1}{4}$$
$$12b\times \frac{1}{\frac{1}{2}}-12=\frac{1}{6}\times \frac{1}{4}\times 12b$$
$$12b\times 1\times 2-12=\frac{1}{6}\times \frac{1}{4}\times 12b$$
$$12b\times 2-12=\frac{1}{6}\times \frac{1}{4}\times 12b$$
$$24b-12=\frac{1}{6}\times \frac{1}{4}\times 12b$$
$$24b-12=\frac{1}{24}\times 12b$$
$$24b-12=\frac{1}{2}b$$
$$24b-12-\frac{1}{2}b=0$$
$$\frac{47}{2}b-12=0$$
$$\frac{47}{2}b=12$$
$$b=12\times \frac{2}{47}$$
$$b=\frac{24}{47}$$
$$a=\frac{1}{2}$$ $$b=\frac{24}{47}$$ $$c=6$$
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