Question 1124733
<font color="black" face="times" size="3">The denominators are a, b and c. The lowest common denominator LCD is the product of all three values: a*b*c


If we multiply everything by the LCD, then the denominators cancel out making the fractions go away.


{{{1/a = 1/b - 1/c}}}


{{{a*b*c*(1/a) = a*b*c*(1/b) - a*b*c*(1/c)}}} Multiply each of the three terms by the LCD a*b*c


{{{highlight(a)*b*c*(1/(highlight(a))) = a*highlight(b)*c*(1/(highlight(b))) - a*b*highlight(c)*(1/(highlight(c)))}}} Notice these pairs match up


{{{cross(a)*b*c*(1/(cross(a))) = a*cross(b)*c*(1/(cross(b))) - a*b*cross(c)*(1/(cross(c)))}}} Those same pairs divide and cancel out (since x/x = 1 where x is nonzero)


{{{b*c = a*c - a*b}}} The fractions are gone at this point. Let's isolate c


{{{b*c - a*c  = -a*b}}} Subtract ac from both sides


{{{c(b - a)  = -a*b}}} Factor out the common factor c


{{{c  = (-a*b)/(b - a)}}} Divide both sides by (b-a)


The answer is {{{c  = (-a*b)/(b - a)}}}</font>