I'm studying for the GRE and am a bit confused about when it is permissible to take the reciprocal of both sides of the equations in order to solve for a variable and when it's not. For example, the study book I'm using said that if you're trying to find "1/a= 1/b + 1/c," you can't just take the reciprocal of both sides, i.e., it's not just a= b +c, but first must add "1/b" and "1/c" to get (b+c/bc)= 1/a, and then you can take the reciprocal to get a=bc/b+c. OR for (1/a-b)=5, just take the reciprocal to find a-b=1/5, so a=b+1/5. So my question is, what is the general rule about when it is ok to take the reciprocal of both sides of the equation? what are the conditions? How come in the above example you couldn't take the reciprocal with the first problem until the two fractions were added together? Thank you for your time.