Question

Solve for c; 1/a-1/b-1/c-=4

Answer 1

`a\\e0,\ b\\eq0,\ c\\eq0\\\\(1)/(a)-(1)/(b)-(1)/(c)=4\qquad\text{multiply both sides by ab}\\\\\\ot a^1b\cdot(1)/(\\ot a_1)-a\\ot b^1\cdot(1)/(\\ot b_1)-ab\cdot(1)/(c)=4ab\\\\b-a-(ab)/(c)=4ab\qquad\text{subtract b from both sides}\\\\-a-(ab)/(c)=4ab-b\qquad\text{add a to both sides}\\\\-(ab)/(c)=4ab+a-b\qquad\text{change the signs}\\\\(ab)/(c)=b-4ab-a\qquad\text{reciprocal of both sides}`

`(c)/(ab)=(1)/(b-4ab-a)\qquad\text{multiply both sides by ab}\\\\\boxed{c=(ab)/(b-4ab-a)}`