Even though fraction bars do not fit into the PEMDAS hierarchy, they do take precedence. In any expression with a fraction bar, you should pretend that there are parentheses around the numerator and denominator of the fraction. This may be obvious as long as the fraction bar remains in the expression, but it is easy to forget if you eliminate the fraction bar or add or subtract fractions, so put parentheses in to remind yourself:
The common denominator for the two fractions is 6, so multiply the numerator and denominator of the first fraction by 3, and those of the second fraction by 2:
Once you put all numerators over the common denominator, the parentheses remind you to reverse the signs of both terms in the second numerator:
In that last step, the minus sign was pulled out from both the x and the 1 and put in front of the fraction. You can do this because −x − 1 is the same thing as −(x + 1). Again, the fraction bar is working as a grouping symbol.
Simplify:
