Question 708022
Starting with {{{(c/x)+(m/a)=c}}}, 


For finding a,
notice a lowest common denominator of xa.  Multiply left and right hand members by xa.


{{{xa(c/x)+xa(m/a)=xac}}}
{{{ac+xm=xac}}}
{{{ac+xm=axc}}}  [commutative prop. multip.]
{{{ac-ac+xm=axc-ac}}}
{{{xm=a(xc-c)}}}
{{{xm(xc-c)^(-1)=a(xc-c)(xc-c)^(-1)}}}, [multiplicative inverse]
{{{xm/(xc-c)=a*1}}}
{{{highlight(a=xm/(xc-c))}}}