Question 57746
{{{r=ab/(a+b)}}} ;a  solve for a
{{{r(a+b)=ab(a+b)/(a+b)}}}  Multiply both sides by LCD.
{{{ra+rb=ab}}}  Get all the a's on one side of the = sign
{{{ra-ab+rb=ab-ab}}}  
{{{ra-ab+rb=0}}}  Get the things without a's on the other side of the = sign.
{{{ra-ab+rb-rb=0-rb}}}
{{{ra-ab=-rb}}}  Factor out the a on the left.
{{{a(r-b)=-rb}}}  Divide both sides by r-b.
{{{a(r-b)/(r-b)=-rb/(r-b)}}}
{{{a=-rb/(r-b)}}}  it could be written as:  {{{a=rb/(b-r)}}}
Happy Calculating!!!