[tex]a\ne0,\ b\neq0,\ c\neq0\\\\\dfrac{1}{a}-\dfrac{1}{b}-\dfrac{1}{c}=4\qquad\text{multiply both sides by ab}\\\\\not a^1b\cdot\dfrac{1}{\not a_1}-a\not b^1\cdot\dfrac{1}{\not b_1}-ab\cdot\dfrac{1}{c}=4ab\\\\b-a-\dfrac{ab}{c}=4ab\qquad\text{subtract b from both sides}\\\\-a-\dfrac{ab}{c}=4ab-b\qquad\text{add a to both sides}\\\\-\dfrac{ab}{c}=4ab+a-b\qquad\text{change the signs}\\\\\dfrac{ab}{c}=b-4ab-a\qquad\text{reciprocal of both sides}[/tex]
[tex]\dfrac{c}{ab}=\dfrac{1}{b-4ab-a}\qquad\text{multiply both sides by ab}\\\\\boxed{c=\dfrac{ab}{b-4ab-a}}[/tex]
