Question 165590
If:
{{{(1/x)+(1/a) = 1/b}}} {{{a<>0}}} Find x:
{{{(1/x)+(1/a) = 1/b}}} Subtract {{{1/a}}} from both sides.
{{{1/x = (1/b)-(1/a)}}} Subtract the fractions on the right side and simplify, LCD is {{{ab}}}
{{{1/x = (a-b)/(ab)}}} Multiply both sides by x.
{{{1 = x(a-b)/(ab)}}} Multiply both sides by {{{ab}}}
{{{ab = x(a-b)}}} Finally, divide both sides by {{{(a-b)}}}
{{{ab/((a-b)) = x}}} or {{{highlight(x = ab/((a-b)))}}}